Deck 9: Infinite Series

ملء الشاشة (f)
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سؤال
Write out terms Write out terms   of the given sequence.  <div style=padding-top: 35px> of the given sequence. Write out terms   of the given sequence.  <div style=padding-top: 35px>
استخدم زر المسافة أو
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لقلب البطاقة.
سؤال
Determine whether Determine whether   converges or diverges. Show all your work.<div style=padding-top: 35px> converges or diverges. Show all your work.
سؤال
Determine whether the series converges or diverges. If it converges, find its sum. <strong>Determine whether the series converges or diverges. If it converges, find its sum.  </strong> A) 7 B)   C)   D) diverges <div style=padding-top: 35px>

A) 7
B) <strong>Determine whether the series converges or diverges. If it converges, find its sum.  </strong> A) 7 B)   C)   D) diverges <div style=padding-top: 35px>
C) <strong>Determine whether the series converges or diverges. If it converges, find its sum.  </strong> A) 7 B)   C)   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Show that Show that   is bounded. Show all your work.<div style=padding-top: 35px> is bounded. Show all your work.
سؤال
Write a formula that produces the given terms of the sequence. <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> , <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> , <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Evaluate the limit. <strong>Evaluate the limit.  </strong> A) 9 B) 0 C) 1 D) limit does not exist <div style=padding-top: 35px>

A) 9
B) 0
C) 1
D) limit does not exist
سؤال
Determine whether <strong>Determine whether   is increasing, decreasing or neither.</strong> A) decreasing B) increasing C) neither <div style=padding-top: 35px> is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither
سؤال
Determine whether the sequence converges or diverges. <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to   C) converges to   D) diverges <div style=padding-top: 35px>

A) converges to 0
B) converges to <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to   C) converges to   D) diverges <div style=padding-top: 35px>
C) converges to <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to   C) converges to   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Find the limit of the sequence <strong>Find the limit of the sequence   .</strong> A) -7 B) 0 C) 7 D) does not exist <div style=padding-top: 35px> .

A) -7
B) 0
C) 7
D) does not exist
سؤال
Find the limit of the sequence. <strong>Find the limit of the sequence.  </strong> A) 1 B)   C) 7 D) 5 <div style=padding-top: 35px>

A) 1
B) <strong>Find the limit of the sequence.  </strong> A) 1 B)   C) 7 D) 5 <div style=padding-top: 35px>
C) 7
D) 5
سؤال
Determine whether Determine whether   converges or diverges. Show all your work.<div style=padding-top: 35px> converges or diverges. Show all your work.
سؤال
Determine whether the sequence converges or diverges. <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to 1 C) converges to   D) diverges <div style=padding-top: 35px>

A) converges to 0
B) converges to 1
C) converges to <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to 1 C) converges to   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Determine whether <strong>Determine whether   is increasing, decreasing or neither.</strong> A) decreasing B) increasing C) neither <div style=padding-top: 35px> is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither
سؤال
Show that Show that   is bounded. Show all your work.<div style=padding-top: 35px> is bounded. Show all your work.
سؤال
Write out terms Write out terms   of the given sequence.  <div style=padding-top: 35px> of the given sequence. Write out terms   of the given sequence.  <div style=padding-top: 35px>
سؤال
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px> converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Find the limit of the sequence <strong>Find the limit of the sequence   .</strong> A) 0 B) 9 C)   D) does not exist <div style=padding-top: 35px> .

A) 0
B) 9
C) <strong>Find the limit of the sequence   .</strong> A) 0 B) 9 C)   D) does not exist <div style=padding-top: 35px>
D) does not exist
سؤال
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px> converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Determine whether Determine whether   converges or diverges. Show all your work.<div style=padding-top: 35px> converges or diverges. Show all your work.
سؤال
Write a formula that produces the given terms of the sequence. <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> , <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> , <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px> , <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine convergence or divergence of the series. Determine convergence or divergence of the series.  <div style=padding-top: 35px>
سؤال
Determine all values of p for which the series <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px> converges.

A) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine all values of c such that the series converges. <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval   <div style=padding-top: 35px>

A) <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval   <div style=padding-top: 35px> any real number
B) c in the interval <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval   <div style=padding-top: 35px>
C) c in the interval <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval   <div style=padding-top: 35px>
D) c in the interval <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval   <div style=padding-top: 35px>
سؤال
Estimate the error in using Estimate the error in using   to approximate the sum of   . Show all your work.<div style=padding-top: 35px> to approximate the sum of Estimate the error in using   to approximate the sum of   . Show all your work.<div style=padding-top: 35px> . Show all your work.
سؤال
Determine all values of p for which the series <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px> converges.

A) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Imagine a ball dropped from a height of 15 feet. Each time it strikes the ground, it bounces 0.6 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.

A) 9 feet
B) 0.4 feet
C) 60 feet
D) 15 feet
سؤال
Determine convergence or divergence of the series. Determine convergence or divergence of the series.  <div style=padding-top: 35px>
سؤال
Use graphical and numerical evidence to conjecture whether the series <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to   <div style=padding-top: 35px> converges or diverges. <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to   <div style=padding-top: 35px> <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to   <div style=padding-top: 35px>

A) diverges
B) converges to 0.9
C) converges to <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to   <div style=padding-top: 35px>
D) converges to <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to   <div style=padding-top: 35px>
سؤال
Determine the convergence or divergence of Determine the convergence or divergence of   . Show all your work.<div style=padding-top: 35px> .
Show all your work.
سؤال
Determine convergence or divergence of the series. Determine convergence or divergence of the series.  <div style=padding-top: 35px>
سؤال
A dosage of 200 mL of a drug is given at times <strong>A dosage of 200 mL of a drug is given at times   . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after   doses is   Find the eventual level of the drug (after an infinite number of doses). Round to the nearest mL.</strong> A) 333 mL B) 500 mL C) 443 mL D) 607 mL <div style=padding-top: 35px> . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after <strong>A dosage of 200 mL of a drug is given at times   . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after   doses is   Find the eventual level of the drug (after an infinite number of doses). Round to the nearest mL.</strong> A) 333 mL B) 500 mL C) 443 mL D) 607 mL <div style=padding-top: 35px> doses is <strong>A dosage of 200 mL of a drug is given at times   . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after   doses is   Find the eventual level of the drug (after an infinite number of doses). Round to the nearest mL.</strong> A) 333 mL B) 500 mL C) 443 mL D) 607 mL <div style=padding-top: 35px> Find the eventual level of the drug (after an "infinite" number of doses). Round to the nearest mL.

A) 333 mL
B) 500 mL
C) 443 mL
D) 607 mL
سؤال
Suppose that the total salary of all the employees at a factory in a certain city is $300,000. Of this salary, 60% is spent in the city. Of the money spent in the city, 60% is again spent in the city. If this continues indefinitely, how much total money is spent in the city, that is, how much of an effect does the original total salary have on the local economy?

A) $1,800,000
B) $288,000
C) $450,000
D) $352,800
سؤال
Determine convergence or divergence of the series. Determine convergence or divergence of the series.  <div style=padding-top: 35px>
سؤال
Estimate the error in using Estimate the error in using   to approximate the sum of   . Show all your work.<div style=padding-top: 35px> to approximate the sum of Estimate the error in using   to approximate the sum of   . Show all your work.<div style=padding-top: 35px> . Show all your work.
سؤال
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px> converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Determine the convergence or divergence of Determine the convergence or divergence of   . Show all your work.<div style=padding-top: 35px> .
Show all your work.
سؤال
Determine the convergence or divergence of Determine the convergence or divergence of   . Show all your work.<div style=padding-top: 35px> .
Show all your work.
سؤال
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px> converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Use graphical and numerical evidence to conjecture whether the series <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px> converges or diverges. . <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px> <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>

A) converges with sum = <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
B) converges with sum = <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
C) converges with sum = <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <div style=padding-top: 35px>
D) diverges
سؤال
Write <strong>Write   as a fraction.</strong> A)   B)   C)   D)   <div style=padding-top: 35px> as a fraction.

A) <strong>Write   as a fraction.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Write   as a fraction.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Write   as a fraction.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Write   as a fraction.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. <strong>Determine whether the series is absolutely convergent, conditionally convergent, or divergent.  </strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px>

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Estimate the error in using Estimate the error in using   to approximate the sum of   . Show all your work.<div style=padding-top: 35px> to approximate the sum of Estimate the error in using   to approximate the sum of   . Show all your work.<div style=padding-top: 35px> . Show all your work.
سؤال
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. <strong>Determine whether the series is absolutely convergent, conditionally convergent, or divergent.  </strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px>

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Determine the number of terms needed to obtain the sum of <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A) 282 B) 200 C) 2,829 D) 2,666,668 <div style=padding-top: 35px> to within 10-6.

A) 282
B) 200
C) 2,829
D) 2,666,668
سؤال
Determine whether the series is convergent or divergent. Determine whether the series is convergent or divergent.  <div style=padding-top: 35px>
سؤال
Determine the number of terms needed to obtain the sum of <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 <div style=padding-top: 35px> to within 10-6.

A) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 <div style=padding-top: 35px> or n = 13
B) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 <div style=padding-top: 35px> or n = 2
C) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 <div style=padding-top: 35px> or n = 4
D) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 <div style=padding-top: 35px> or n = -13
سؤال
Determine if Determine if   converges or diverges. Show your work.<div style=padding-top: 35px> converges or diverges. Show your work.
سؤال
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px> is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px> is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Estimate the sum of <strong>Estimate the sum of   to within 0.01.</strong> A) -0.14 B) -0.18 C) -0.11 D) -0.08 <div style=padding-top: 35px> to within 0.01.

A) -0.14
B) -0.18
C) -0.11
D) -0.08
سؤال
Estimate the sum of <strong>Estimate the sum of   to within 0.01.</strong> A) 0.10 B) 5.00 C) 4.96 D) 0.04 <div style=padding-top: 35px> to within 0.01.

A) 0.10
B) 5.00
C) 4.96
D) 0.04
سؤال
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. <strong>Determine whether the series is absolutely convergent, conditionally convergent, or divergent.  </strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px>

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Determine whether the series is convergent or divergent. Determine whether the series is convergent or divergent.  <div style=padding-top: 35px>
سؤال
Estimate the sum of <strong>Estimate the sum of   to within 0.01.</strong> A) 2.58 B) 2.50 C) 2.53 D) -0.17 <div style=padding-top: 35px> to within 0.01.

A) 2.58
B) 2.50
C) 2.53
D) -0.17
سؤال
Determine how many terms are needed to estimate <strong>Determine how many terms are needed to estimate   to within 0.0001.</strong> A) k = 7 B) k = 8 C) k = 6,999 D) k = 70,000 <div style=padding-top: 35px> to within 0.0001.

A) k = 7
B) k = 8
C) k = 6,999
D) k = 70,000
سؤال
Determine whether the series is convergent or divergent. Determine whether the series is convergent or divergent.  <div style=padding-top: 35px>
سؤال
Determine if Determine if   converges or diverges. Show your work.<div style=padding-top: 35px> converges or diverges. Show your work.
سؤال
Determine how many terms are needed to estimate <strong>Determine how many terms are needed to estimate   to within 0.001.</strong> A) k = 4000 B) k = 28 C) k = 63 D) k = 5 <div style=padding-top: 35px> to within 0.001.

A) k = 4000
B) k = 28
C) k = 63
D) k = 5
سؤال
Determine how many terms are needed to estimate <strong>Determine how many terms are needed to estimate   to within 0.0001.</strong> A) k = 26 B) k = 27 C) k = 8 D) k = 0.9997 <div style=padding-top: 35px> to within 0.0001.

A) k = 26
B) k = 27
C) k = 8
D) k = 0.9997
سؤال
Determine if Determine if   converges or diverges. Show your work.<div style=padding-top: 35px> converges or diverges. Show your work.
سؤال
Determine the radius and interval of convergence. <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>

A) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
B) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
C) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
D) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
سؤال
Find a power series representation and radius of convergence for <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> by integrating or differentiating a series.

A) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
B) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
C) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
D) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
سؤال
Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence. <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px> is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px> is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Find a power series representation and radius of convergence for <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> by integrating or differentiating a series.

A) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
B) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
C) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
D) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px> ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   <div style=padding-top: 35px>
سؤال
Find the interval of convergence and function f(x) to which <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px> converges.

A) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px> is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Determine the radius and interval of convergence. <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px>

A) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px>
B) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px>
C) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px>
D) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px> converges for <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <div style=padding-top: 35px>
سؤال
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent <div style=padding-top: 35px> is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
سؤال
Find the interval of convergence and function f(x) to which <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px> converges.

A) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the MacLaurin series and its interval of convergence. <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine the radius and interval of convergence of <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px> .

A) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find a power series representation of <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px> about <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px> Determine the interval of convergence for the power series.

A) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px>
B) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px>
C) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px>
D) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <div style=padding-top: 35px>
سؤال
Determine the radius and interval of convergence of <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px> .

A) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence. <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine the radius and interval of convergence. <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>

A) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
B) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
C) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
D) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px> <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <div style=padding-top: 35px>
سؤال
Find the interval of convergence of the (non-power) series and the corresponding series of derivatives. <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>

A) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine the radius and interval of convergence of <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px> .

A) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
B) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
C) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
D) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   <div style=padding-top: 35px>
سؤال
Determine the interval of convergence and the function to which the power series converges. Determine the interval of convergence and the function to which the power series converges.  <div style=padding-top: 35px>
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Deck 9: Infinite Series
1
Write out terms Write out terms   of the given sequence.  of the given sequence. Write out terms   of the given sequence.
    ,   ,      ,   ,  ,     ,   ,  ,     ,   ,
2
Determine whether Determine whether   converges or diverges. Show all your work. converges or diverges. Show all your work.
  ; the limit does not exist, so the sequence diverges. ; the limit does not exist, so the sequence diverges.
3
Determine whether the series converges or diverges. If it converges, find its sum. <strong>Determine whether the series converges or diverges. If it converges, find its sum.  </strong> A) 7 B)   C)   D) diverges

A) 7
B) <strong>Determine whether the series converges or diverges. If it converges, find its sum.  </strong> A) 7 B)   C)   D) diverges
C) <strong>Determine whether the series converges or diverges. If it converges, find its sum.  </strong> A) 7 B)   C)   D) diverges
D) diverges
B
4
Show that Show that   is bounded. Show all your work. is bounded. Show all your work.
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5
Write a formula that produces the given terms of the sequence. <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   , <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)   , <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)

A) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)
B) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)
C) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)
D) <strong>Write a formula that produces the given terms of the sequence.     ,   ,  </strong> A)   B)   C)   D)
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6
Evaluate the limit. <strong>Evaluate the limit.  </strong> A) 9 B) 0 C) 1 D) limit does not exist

A) 9
B) 0
C) 1
D) limit does not exist
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7
Determine whether <strong>Determine whether   is increasing, decreasing or neither.</strong> A) decreasing B) increasing C) neither is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither
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8
Determine whether the sequence converges or diverges. <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to   C) converges to   D) diverges

A) converges to 0
B) converges to <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to   C) converges to   D) diverges
C) converges to <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to   C) converges to   D) diverges
D) diverges
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9
Find the limit of the sequence <strong>Find the limit of the sequence   .</strong> A) -7 B) 0 C) 7 D) does not exist .

A) -7
B) 0
C) 7
D) does not exist
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10
Find the limit of the sequence. <strong>Find the limit of the sequence.  </strong> A) 1 B)   C) 7 D) 5

A) 1
B) <strong>Find the limit of the sequence.  </strong> A) 1 B)   C) 7 D) 5
C) 7
D) 5
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11
Determine whether Determine whether   converges or diverges. Show all your work. converges or diverges. Show all your work.
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12
Determine whether the sequence converges or diverges. <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to 1 C) converges to   D) diverges

A) converges to 0
B) converges to 1
C) converges to <strong>Determine whether the sequence converges or diverges.  </strong> A) converges to 0 B) converges to 1 C) converges to   D) diverges
D) diverges
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13
Determine whether <strong>Determine whether   is increasing, decreasing or neither.</strong> A) decreasing B) increasing C) neither is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither
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14
Show that Show that   is bounded. Show all your work. is bounded. Show all your work.
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15
Write out terms Write out terms   of the given sequence.  of the given sequence. Write out terms   of the given sequence.
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16
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
D) diverges
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17
Find the limit of the sequence <strong>Find the limit of the sequence   .</strong> A) 0 B) 9 C)   D) does not exist .

A) 0
B) 9
C) <strong>Find the limit of the sequence   .</strong> A) 0 B) 9 C)   D) does not exist
D) does not exist
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18
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
D) diverges
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19
Determine whether Determine whether   converges or diverges. Show all your work. converges or diverges. Show all your work.
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20
Write a formula that produces the given terms of the sequence. <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   , <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   , <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)   , <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)

A) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)
B) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)
C) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)
D) <strong>Write a formula that produces the given terms of the sequence.     ,   ,   ,  </strong> A)   B)   C)   D)
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21
Determine convergence or divergence of the series. Determine convergence or divergence of the series.
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22
Determine all values of p for which the series <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   converges.

A) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
B) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
C) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
D) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
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23
Determine all values of c such that the series converges. <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval

A) <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval   any real number
B) c in the interval <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval
C) c in the interval <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval
D) c in the interval <strong>Determine all values of c such that the series converges.  </strong> A)   any real number B) c in the interval   C) c in the interval   D) c in the interval
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24
Estimate the error in using Estimate the error in using   to approximate the sum of   . Show all your work. to approximate the sum of Estimate the error in using   to approximate the sum of   . Show all your work. . Show all your work.
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25
Determine all values of p for which the series <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)   converges.

A) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
B) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
C) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
D) <strong>Determine all values of p for which the series   converges.</strong> A)   B)   C)   D)
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26
Imagine a ball dropped from a height of 15 feet. Each time it strikes the ground, it bounces 0.6 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.

A) 9 feet
B) 0.4 feet
C) 60 feet
D) 15 feet
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27
Determine convergence or divergence of the series. Determine convergence or divergence of the series.
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28
Use graphical and numerical evidence to conjecture whether the series <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to   converges or diverges. <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to   <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to

A) diverges
B) converges to 0.9
C) converges to <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to
D) converges to <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges.    </strong> A) diverges B) converges to 0.9 C) converges to   D) converges to
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29
Determine the convergence or divergence of Determine the convergence or divergence of   . Show all your work. .
Show all your work.
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30
Determine convergence or divergence of the series. Determine convergence or divergence of the series.
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31
A dosage of 200 mL of a drug is given at times <strong>A dosage of 200 mL of a drug is given at times   . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after   doses is   Find the eventual level of the drug (after an infinite number of doses). Round to the nearest mL.</strong> A) 333 mL B) 500 mL C) 443 mL D) 607 mL . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after <strong>A dosage of 200 mL of a drug is given at times   . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after   doses is   Find the eventual level of the drug (after an infinite number of doses). Round to the nearest mL.</strong> A) 333 mL B) 500 mL C) 443 mL D) 607 mL doses is <strong>A dosage of 200 mL of a drug is given at times   . The drug decays exponentially with rate 0.6 in the bloodstream. The amount in the bloodstream after   doses is   Find the eventual level of the drug (after an infinite number of doses). Round to the nearest mL.</strong> A) 333 mL B) 500 mL C) 443 mL D) 607 mL Find the eventual level of the drug (after an "infinite" number of doses). Round to the nearest mL.

A) 333 mL
B) 500 mL
C) 443 mL
D) 607 mL
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32
Suppose that the total salary of all the employees at a factory in a certain city is $300,000. Of this salary, 60% is spent in the city. Of the money spent in the city, 60% is again spent in the city. If this continues indefinitely, how much total money is spent in the city, that is, how much of an effect does the original total salary have on the local economy?

A) $1,800,000
B) $288,000
C) $450,000
D) $352,800
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33
Determine convergence or divergence of the series. Determine convergence or divergence of the series.
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34
Estimate the error in using Estimate the error in using   to approximate the sum of   . Show all your work. to approximate the sum of Estimate the error in using   to approximate the sum of   . Show all your work. . Show all your work.
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35
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
D) diverges
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36
Determine the convergence or divergence of Determine the convergence or divergence of   . Show all your work. .
Show all your work.
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37
Determine the convergence or divergence of Determine the convergence or divergence of   . Show all your work. .
Show all your work.
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38
Determine if <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges converges or diverges. If convergent, find the sum of the series.

A) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
B) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
C) converges with sum = <strong>Determine if   converges or diverges. If convergent, find the sum of the series.</strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
D) diverges
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39
Use graphical and numerical evidence to conjecture whether the series <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges converges or diverges. . <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges

A) converges with sum = <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
B) converges with sum = <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
C) converges with sum = <strong>Use graphical and numerical evidence to conjecture whether the series   converges or diverges. .    </strong> A) converges with sum =   B) converges with sum =   C) converges with sum =   D) diverges
D) diverges
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40
Write <strong>Write   as a fraction.</strong> A)   B)   C)   D)   as a fraction.

A) <strong>Write   as a fraction.</strong> A)   B)   C)   D)
B) <strong>Write   as a fraction.</strong> A)   B)   C)   D)
C) <strong>Write   as a fraction.</strong> A)   B)   C)   D)
D) <strong>Write   as a fraction.</strong> A)   B)   C)   D)
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41
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. <strong>Determine whether the series is absolutely convergent, conditionally convergent, or divergent.  </strong> A) absolutely convergent B) conditionally convergent C) divergent

A) absolutely convergent
B) conditionally convergent
C) divergent
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42
Estimate the error in using Estimate the error in using   to approximate the sum of   . Show all your work. to approximate the sum of Estimate the error in using   to approximate the sum of   . Show all your work. . Show all your work.
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43
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. <strong>Determine whether the series is absolutely convergent, conditionally convergent, or divergent.  </strong> A) absolutely convergent B) conditionally convergent C) divergent

A) absolutely convergent
B) conditionally convergent
C) divergent
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44
Determine the number of terms needed to obtain the sum of <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A) 282 B) 200 C) 2,829 D) 2,666,668 to within 10-6.

A) 282
B) 200
C) 2,829
D) 2,666,668
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45
Determine whether the series is convergent or divergent. Determine whether the series is convergent or divergent.
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46
Determine the number of terms needed to obtain the sum of <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 to within 10-6.

A) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 or n = 13
B) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 or n = 2
C) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 or n = 4
D) <strong>Determine the number of terms needed to obtain the sum of   to within 10<sup>-6</sup>.</strong> A)   or n = 13 B)   or n = 2 C)   or n = 4 D)   or n = -13 or n = -13
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47
Determine if Determine if   converges or diverges. Show your work. converges or diverges. Show your work.
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48
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
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49
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
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50
Estimate the sum of <strong>Estimate the sum of   to within 0.01.</strong> A) -0.14 B) -0.18 C) -0.11 D) -0.08 to within 0.01.

A) -0.14
B) -0.18
C) -0.11
D) -0.08
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51
Estimate the sum of <strong>Estimate the sum of   to within 0.01.</strong> A) 0.10 B) 5.00 C) 4.96 D) 0.04 to within 0.01.

A) 0.10
B) 5.00
C) 4.96
D) 0.04
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52
Determine whether the series is absolutely convergent, conditionally convergent, or divergent. <strong>Determine whether the series is absolutely convergent, conditionally convergent, or divergent.  </strong> A) absolutely convergent B) conditionally convergent C) divergent

A) absolutely convergent
B) conditionally convergent
C) divergent
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53
Determine whether the series is convergent or divergent. Determine whether the series is convergent or divergent.
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54
Estimate the sum of <strong>Estimate the sum of   to within 0.01.</strong> A) 2.58 B) 2.50 C) 2.53 D) -0.17 to within 0.01.

A) 2.58
B) 2.50
C) 2.53
D) -0.17
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55
Determine how many terms are needed to estimate <strong>Determine how many terms are needed to estimate   to within 0.0001.</strong> A) k = 7 B) k = 8 C) k = 6,999 D) k = 70,000 to within 0.0001.

A) k = 7
B) k = 8
C) k = 6,999
D) k = 70,000
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56
Determine whether the series is convergent or divergent. Determine whether the series is convergent or divergent.
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57
Determine if Determine if   converges or diverges. Show your work. converges or diverges. Show your work.
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58
Determine how many terms are needed to estimate <strong>Determine how many terms are needed to estimate   to within 0.001.</strong> A) k = 4000 B) k = 28 C) k = 63 D) k = 5 to within 0.001.

A) k = 4000
B) k = 28
C) k = 63
D) k = 5
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59
Determine how many terms are needed to estimate <strong>Determine how many terms are needed to estimate   to within 0.0001.</strong> A) k = 26 B) k = 27 C) k = 8 D) k = 0.9997 to within 0.0001.

A) k = 26
B) k = 27
C) k = 8
D) k = 0.9997
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60
Determine if Determine if   converges or diverges. Show your work. converges or diverges. Show your work.
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61
Determine the radius and interval of convergence. <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)

A) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
B) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
C) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
D) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
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62
Find a power series representation and radius of convergence for <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   by integrating or differentiating a series.

A) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
B) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
C) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
D) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
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63
Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence. <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)

A) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
B) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
C) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
D) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
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64
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
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65
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
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66
Find a power series representation and radius of convergence for <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   by integrating or differentiating a series.

A) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
B) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
C) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
D) <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;   ; <strong>Find a power series representation and radius of convergence for   by integrating or differentiating a series.</strong> A)   ;   B)   ;   C)   ;   D)   ;
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67
Find the interval of convergence and function f(x) to which <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   converges.

A) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
B) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
C) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
D) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
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68
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
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69
Determine the radius and interval of convergence. <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for

A) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for
B) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for
C) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for
D) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for   converges for <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)   converges for
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70
Determine if <strong>Determine if   is absolutely convergent, conditionally convergent or divergent.</strong> A) absolutely convergent B) conditionally convergent C) divergent is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent
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71
Find the interval of convergence and function f(x) to which <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)   converges.

A) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
B) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
C) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
D) <strong>Find the interval of convergence and function f(x) to which   converges.</strong> A)   B)   C)   D)
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72
Find the MacLaurin series and its interval of convergence. <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)

A) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)
B) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)
C) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)
D) <strong>Find the MacLaurin series and its interval of convergence.  </strong> A)   B)   C)   D)
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73
Determine the radius and interval of convergence of <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   .

A) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
B) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
C) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
D) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
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74
Find a power series representation of <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     about <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     Determine the interval of convergence for the power series.

A) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)
B) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)
C) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)
D) <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)     <strong>Find a power series representation of   about   Determine the interval of convergence for the power series.</strong> A)     B)     C)     D)
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75
Determine the radius and interval of convergence of <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   .

A) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
B) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
C) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
D) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
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76
Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence. <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)

A) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
B) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
C) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
D) <strong>Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.  </strong> A)   B)   C)   D)
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77
Determine the radius and interval of convergence. <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)

A) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
B) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
C) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
D) <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)     <strong>Determine the radius and interval of convergence.  </strong> A)     B)     C)     D)
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78
Find the interval of convergence of the (non-power) series and the corresponding series of derivatives. <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)

A) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)
B) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)
C) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)
D) <strong>Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.  </strong> A)   B)   C)   D)
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79
Determine the radius and interval of convergence of <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)   .

A) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
B) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
C) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
D) <strong>Determine the radius and interval of convergence of   .</strong> A)   B)   C)   D)
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80
Determine the interval of convergence and the function to which the power series converges. Determine the interval of convergence and the function to which the power series converges.
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