Deck 9: Section 5: Infinite Series

Question 1

The series is a convergent series. Use Theorem 9.15 to determine the number of terms required to approximate the sum of this series with an error less than 0.001.

A)
B)
C)
D)
E)

Answer 1

Question 2

Use the Alternating Series Test (if possible) to determine whether the series converges or diverges?

A)
B)
C) Alternating Series Test cannot be applied

Answer 2

Question 3

Determine whether the series converges conditionally or absolutely, or diverges.

A) The series converges conditionally but does not converge absolutely.
B) The series converges absolutely but does not converge conditionally.
C) The series diverges.
D) The series converges absolutely.

Answer 3

The series converges conditionally but does not converge absolutely.

Question 4

Consider the series . Review the Alternating Series Test to determine which of the following statements is true for the given series.

A) Since for some n, the series diverges.
B) Since cannot be shown to be true for all n, the Alternating Series Test cannot be applied.
C) The series converges.
D) Since cannot be shown to be true for all n, the series diverges.
E) Since , the series diverges.

Question 5

Determine whether the series converges absolutely, converges conditionally, or diverges.

A) converges absolutely
B) diverges
C) converges conditionally

Question 6

Consider the series . Review the Alternating Series Test to determine which of the following statements is true for the given series.

A) Since , the series diverges.
B) Since , the Alternating Series Test cannot be applied.
C) Since for some n, the Alternating Series Test cannot be applied.
D) Since for some n, the series diverges.
E) The series converges.

Question 7

It can be shown that According to Theorem 9.15, the partial sum approximates with error less than how much?

A)
B)
C)
D)
E)

Question 8

True or false: The series converges.

A)
B)

Question 9

True or false: The series diverges.

A)
B)

Question 10

Determine whether the series converges conditionally or absolutely, or diverges.

A) The series converges absolutely.
B) The series diverges.
C) The series converges absolutely but does not converge conditionally.
D) The series converges conditionally but does not converge absolutely.

Question 11

True or false: The series converges .

A)
B)

Question 12

Determine whether the series converges conditionally or absolutely, or diverges.

A) The series converges absolutely.
B) The series diverges.
C) The series converges absolutely but does not converge conditionally.
D) The series converges conditionally but does not converge absolutely.

Question 13

Determine whether the series converges absolutely, converges conditionally, or diverges.

A)
B) diverges
C)

Question 14

Determine whether the series converges absolutely, converges conditionally, or diverges.

A)
B) converges conditionally
C)

Question 15

True or false: The series diverges.

A)
B)