Deck 8: Series

Question 1

Use multiplication or division of power series to find the first three nonzero terms in the Maclaurin series for the function.

A)
B)
C)
D)
E)

Answer 1

Question 2

Find a power series representation for the function and determine the radius of convergence

A)
B)
C)
D)
E)

Answer 2

Question 3

Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Answer 3

Question 4

Find the Maclaurin series for f (x) using the definition of the Maclaurin series.

A)
B)
C)
D)
E)

Question 5

Use the binomial series to expand the function as a power series.Find the radius of convergence.

Question 6

Find the Taylor polynomial for the function centered at the number a.Graph and on the same screen.

A)
B)
C)
D)

Question 7

Approximate by a Taylor polynomial with degree n at the number a.

A)
B)
C)
D)
E)

Question 8

Find a power series representation for the function and determine the interval of convergence

A)
B)
C)
D)
E)

Question 9

Find the Taylor series for centered at the given value of
a.Assume that f has a power series expansion.Also find the associated radius of convergence.

Question 10

Approximate by a Taylor polynomial with degree n at the number a.

A)
B)
C)
D)
E)

Question 11

Find the sum of the series.

Question 12

Find a power series representation for the function and determine the interval of convergence

A)
B)
C)
D)
E)

Question 13

Find a power series representation for the function and determine the interval of convergence

A)
B)
C)
D)
E)

Question 14

Evaluate the indefinite integral as an infinite series.

Question 15

Find a power series representation for the function and determine the interval of convergence

A)
B)
C)
D)
E)

Question 16

Find the Taylor polynomial for the function centered at the number a.

A)
B)
C)
D)
E)

Question 17

Find the Maclaurin series for using the definition of a Maclaurin series.

Question 18

Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 19

Find the interval of convergence of the series.

A) diverges everywhere
B)
C)
D)
E)

Question 20

Approximate by a Taylor polynomial with degree n at the number a.

A)
B)
C)
D)
E)

Question 21

For which positive integers k is the series convergent?

A)
B)
C)
D)
E)

Question 22

Use the Integral Test to determine whether the series is convergent or divergent.

Question 23

Which of the given series are absolutely convergent?

A)
B)

Question 24

Use the Comparison Test to determine whether the series is convergent or divergent.

Question 25

Find the radius of convergence and the interval of convergence of the power series.

Question 26

Determine whether the series is convergent or divergent.

Question 27

Determine whether the series is absolutely convergent,conditionally convergent,or divergent.

Question 28

Determine whether the geometric series converges or diverges.If it converges,find its sum.

A)
B)
C)
D) Diverges

Question 29

Determine whether the series is absolutely convergent,conditionally convergent,or divergent.

A) absolutely convergent
B) divergent
C) conditionally convergent

Question 30

Determine whether the series is convergent or divergent by expressing as a telescoping sum.If it is convergent,find its sum. .

A)
B)
C)
D)
E) diverges

Question 31

Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 32

Determine whether the given series is convergent or divergent.

Question 33

Find the radius of convergence of the series.

A)
B)
C)
D)
E)

Question 34

Determine whether the given series converges or diverges.If it converges,find its sum.

A)
B)
C) 1
D) Diverges

Question 35

Determine whether the given series converges or diverges.If it converges,find its sum.

A)
B)
C)
D) Diverges

Question 36

Determine whether the series is absolutely convergent,conditionally convergent,or divergent.

A) absolutely convergent
B) divergent
C) conditionally convergent

Question 37

Express the number as a ratio of integers.

Question 38

Determine whether the series is convergent or divergent.

Question 39

Use the sum of the first 10 terms to approximate the sum of the series.Estimate the error.

Question 40

Find all positive values of u for which the series converges.

A)
B)
C)
D)
E)

Question 41

A right triangle ABC is given with and .CD is drawn perpendicular to AB,DE is drawn perpendicular to BC,EF AB and this process is continued indefinitely as shown in the figure.Find the total length of all the perpendiculars Write your answer to two decimal places.

Question 42

Determine whether the sequence defined by converges or diverges.If it converges,find its limit.

A) -5
B)
C)
D) Diverges

Question 43

Determine whether the sequence defined by converges or diverges.If it converges,find its limit.

A) 1
B) 0
C)
D) Diverges

Question 44

Determine whether the given series converges or diverges.If it converges,find its sum.

Question 45

Determine whether the sequence defined by converges or diverges.If it converges,find its limit.

Question 46

Determine whether the sequence defined by converges or diverges.If it converges,find its limit.

A) 1
B) 0
C)
D) Diverges

Question 47

A sequence is defined recursively by the equation for where .Use your calculator to guess the limit of the sequence.

Question 48

If $600 is invested at 4% interest,compounded annually,then after n years the investment is worth dollars.Find the size of investment after 7 years.

A) $789.56
B) $430.21
C) $1,321.06
D) $1,230.81
E) $1,860.81

Question 49

Express the number as a rational number.

Question 50

Determine whether the sequence is increasing,decreasing,or not monotonic.Is the sequence bounded?

A) decreasing
B) increasing
C) not monotonic
D) bounded