Deck 11: Infinite Sequences and Series

Question 1

Evaluate the indefinite integral as an infinite series.

Answer 1

Question 2

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.

Answer 2

Question 3

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

Answer 3

Question 4

Find a power series representation for the indefinite integral.

Question 5

Find the Maclaurin series for f and its radius of convergence.

Question 6

Given the series estimate the error in using the partial sum by comparison with the series .

A)
B)
C)
D)
E)

Question 7

Evaluate the indefinite integral as a power series.

A)
B)
C)
D)
E)

Question 8

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

A)
B)
C)
D)
E)

Question 9

Use series to evaluate the limit correct to three decimal places. Select the correct answer.

A)118.933
B)114.333
C)114.133
D)34.3233
E)115.933

Question 10

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

Question 11

Find a power series representation for the function.

A)
B)
C)
D)
E)

Question 12

Find the sum of the series.

Question 13

Use the power series for to estimate correct to four decimal places.

A)
B)
C)
D)
E)

Question 14

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)

Question 15

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

A)
B)
C)
D)
E)

Question 16

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

Question 17

Use series to approximate the definite integral to within the indicated accuracy.

A)0.0125
B)0.2774
C)0.1447
D)0.0354
E)0.0625

Question 18

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

A)
B)
C)
D)

Question 19

Evaluate the function by a Taylor polynomial of degree centered at , and .

A)
B)
C)
D)
E)

Question 20

Find a power series representation for

A)
B)
C)
D)
E)

Question 21

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

Question 22

Determine whether the series is convergent or divergent.

Question 23

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

Question 24

Find the radius of convergence of the series.

A)
B)
C)
D)
E)

Question 25

Determine whether the series converges or diverges.

Question 26

Test the series for convergence or divergence.

Question 27

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

A)
B)
C)
D)

Question 28

Find the interval of convergence of the series.

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

Question 29

Find the interval of convergence of the series.

Question 30

Determine whether the series is convergent or divergent.

Question 31

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

A)
B)
C)
D)

Question 32

Test the series for convergence or divergence.

Question 33

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

Question 34

Suppose that the radius of convergence of the power series is . What is the radius of convergence of the power series .

A)
B)
C)
D)
E)

Question 35

Find the radius of convergence of the series.

A)
B)
C)
D)
E)

Question 36

Test the series for convergence or divergence.

Question 37

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

A)
B)
C)
D)

Question 38

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

A)
B)
C)
D)

Question 39

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

A)
B)
C)
D)

Question 40

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

A)
B)
C)
D)

Question 41

Which of the given series are absolutely convergent?

A)
B)

Question 42

Determine whether the series converges or diverges.

Question 43

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

Question 44

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

A)absolutely convergent
B)conditionally convergent
C)divergent

Question 45

Determine whether the series converges or diverges.

Question 46

Test the series for convergence or divergence.

Question 47

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

A)absolutely convergent
B)conditionally convergent
C)divergent

Question 48

Determine whether the series converges or diverges.

Question 49

Determine whether the series converges or diverges.

Question 50

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

Question 51

Determine whether the series is convergent or divergent.

Question 52

Determine whether the series converges or diverges.

Question 53

Use the sum of the first 9 terms to approximate the sum of the following series. Write your answer to six decimal places.

Question 54

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

Question 55

Determine whether the series converges or diverges.

Question 56

Find the partial sum of the series . Give your answer to five decimal places.

A)
B)
C)
D)
E)

Question 57

Test the series for convergence or divergence.

Question 58

Determine whether the series is convergent or divergent.

Question 59

For which positive integers k is the series convergent?

A)
B)
C)
D)
E)

Question 60

Determine whether the series is convergent or divergent.

Question 61

Test the series for convergence or divergence.

Question 62

Test the series for convergence or divergence.

Question 63

Determine which series is convergent.

A)
B)

Question 64

Determine the number of terms sufficient to obtain the sum of the series accurate to three decimal places.

A)20
B)21
C)22
D)19

Question 65

Find an approximation of the sum of the series accurate to two decimal places.

A)-1.02
B)-1.09
C)-0.87
D)-0.95

Question 66

Determine whether the series is convergent or divergent.

Question 67

Test the series for convergence or divergence.

Question 68

Approximate the sum to the indicated accuracy.

Question 69

Determine whether the series is convergent or divergent.

Question 70

Approximate the sum to the indicated accuracy.

Question 71

Determine whether the series is convergent or divergent.

Question 72

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

Question 73

Let where f is a continuous, positive, and decreasing function on and suppose that is convergent. Defining where and we have that Find the maximum error if the sum of the series is approximated by

A)0.0006
B)0.2
C)0.025
D)0.005

Question 74

Determine whether the sequence convergent or divergent.

A)converges
B)diverges

Question 75

Which of the partial sums of the alternating series are overestimates of the total sum?

A)
B)
C)
D)
E)

Question 76

Approximate the sum to the indicated accuracy. (five decimal places)

A)
B)
C)
D)
E)

Question 77

Use the Alternating Series Estimation Theorem or Taylor's Inequality to estimate the range of values of x for which the given approximation is accurate to within the stated error. Write a such that .

Question 78

Test the series for convergence or divergence.

A)The series is convergent.
B)The series is divergent.

Question 79

Determine whether the series is convergent or divergent.

Question 80

How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

A)
B)
C)
D)
E)