Deck 11: Infinite Sequences and Series

Question 1

Determine whether the series converges or diverges.

Answer 1

Converges

Question 2

Determine whether the series is convergent or divergent.

Answer 2

convergent

Question 3

Find the sum of the series.

Answer 3

Question 4

Test the series for convergence or divergence.

Question 5

Determine whether the series is convergent or divergent.

Question 6

Find an expression for the term of the sequence.(Assume that the pattern continues.)

Question 7

Test the series for convergence or divergence.

Question 8

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

Question 9

Test the series for convergence or divergence.

Question 10

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

Question 11

Determine whether the series is convergent or divergent.

Question 12

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 13

Test the series for convergence or divergence.

Question 14

Determine whether the series converges or diverges.

Question 15

Find a formula for the general term of the sequence, assuming that the pattern of the first few terms continues.

Question 16

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

Question 17

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

Question 18

How many terms of the series would you need to add to find its sum to within 0.02?

Question 19

Determine whether the given series is convergent or divergent.

Question 20

Write the first five terms of the sequence whose term is given.

Question 21

Test the series for convergence or divergence.

Question 22

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

Question 23

The terms of a series are defined recursively by the equations Determine whether converges or diverges.

Question 24

How many terms of the series would you need to add to find its sum to within 0.02?

Question 25

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

Question 26

Find the exact value of the limit of the sequence defined by

Question 27

Test the series for convergence or divergence.

Question 28

Determine whether the sequence convergent or divergent.

Question 29

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

Question 30

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

Question 31

Determine whether the series is convergent or divergent.

Question 32

Express the numb as a ratio of integers.

Question 33

Determine whether the series converges or diverges.

Question 34

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

Question 35

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

Question 36

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.

Question 37

Determine whether the series is convergent or divergent.

Question 38

Determine whether the series is convergent or divergent.

Question 39

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

Question 40

Test the series for convergence or divergence.

Question 41

Select the correct Answer for each question.
Approximate the sum to the indicated accuracy. (five decimal places)

A)
B)
C)
D)
E)

Question 42

Select the correct Answer for each question.
Which of the given series are absolutely convergent?

A)
B)

Question 43

Select the correct Answer for each question.
Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 44

Select the correct Answer for each question.
For which positive integers k is the series convergent?

A)
B)
C)
D)
E)

Question 45

Select the correct Answer for each question.
Find all positive values of for which the series converges.

A)
B)
C)
D)
E)

Question 46

Select the correct Answer for each question.
Use series to approximate the definite integral to within the indicated accuracy.

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

Question 47

Select the correct Answer for each question.
Use the power series for to estimate correct to four decimal places.

A)
B)
C)
D)
E)

Question 48

Select the correct Answer for each question.
Find an approximation of the sum of the series accurate to two decimal places.

A)-1.06
B)-0.84
C)-0.90
D)-0.98

Question 49

Select the correct Answer for each question.
If $600 is invested at interest, compounded annually, then after years the investment is worth dollars.Find the size of investment after 7 years.

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

Question 50

Select the correct Answer for each question.
Determine whether the sequence defined by converges or diverges.If it converges, find its limit.

A)1
B)
C)0
D)Diverges

Question 51

Select the correct Answer for each question.
Determine whether the geometric series converges or diverges.If it converges, find its sum.

A)30
B)36
C)5
D)Diverges

Question 52

Select the correct Answer for each question.
Find a power series representation for

A)
B)
C)
D)
E)

Question 53

Select the correct Answer for each question.
Find the value of the limit for the sequence given.

A)
B)
C)
D)
E)

Question 54

Select the correct Answer for each question.
Determine which one of the p-series below is divergent.

A)
B)
C)
D)

Question 55

Select the correct Answer for each question.
Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 56

Select the correct Answer for each question.
Use series to evaluate the limit correct to three decimal places. Select the correct Answer

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

Question 57

Select the correct Answer for each question.
Determine whether the geometric series converges or diverges.If it converges, find its sum.

A)
B)
C)Diverges
D)

Question 58

Select the correct Answer for each question.
Determine whether the sequence defined by converges or diverges.If it converges, find its limit.

A)
B)
C)
D)Diverges

Question 59

Select the correct Answer for each question.
A sequenceis defined recursively by the equation where Use your calculator to guess the limit of the sequence.

A)
B)14
C)
D)
E)15

Question 60

Select the correct Answer for each question.
Find the interval of convergence of the series.

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

Question 61

Select the correct Answer for each question.
Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 62

Select the correct Answer for each question.
A sequenceis defined recursively by the equation for where Use your calculator to guess the limit of the sequence.

A)
B)14
C)
D)
E)15

Question 63

Select the correct Answer for each question.
Suppose that the radius of convergence of the power series What is the radius of convergence of the power series

A)
B)
C)
D)
E)

Question 64

Select the correct Answer for each question.
Find the Maclaurin series for f (x) using the definition of the Maclaurin series.

A)
B)
C)
D)
E)

Question 65

Select the correct Answer for each question.
Find the sum of the series.

A)
B)
C)
D)
E)

Question 66

Select the correct Answer for each question.
Determine whether the sequence convergent or divergent.

A)converges
B)diverges

Question 67

Select the correct Answer for each question.
Find the radius of convergence and the interval of convergence of the power series.

A)
B)
C)
D)

Question 68

Select the correct Answer for each question.
Find all values of p for which the series converges.

A)
B)
C)
D)

Question 69

Select the correct Answer for each question.
A rubber ball is dropped from a height of 8 m onto a flat surface.Each time the ball hits the surface, it rebounds to 50% of its previous height.Find the total distance the ball travels.

A)16
B)24
C)8
D)32

Question 70

Select the correct Answer for each question.
Find the value of the limit for the sequence given.

A)
B)
C)
D)
E)

Question 71

Select the correct Answer for each question.
Determine whether the series is absolutely convergent, conditionally convergent, or divergent.

A)conditionally convergent
B)absolutely convergent
C)divergent

Question 72

Select the correct Answer for each question.
Find all positive values of u for which the series converges.

A)
B)
C)
D)
E)

Question 73

Select the correct Answer for each question.
Find the values of p for which the series is convergent.

A)
B)
C)
D)

Question 74

Select the correct Answer for each question.
Determine whether the geometric series converges or diverges.If it converges, find its sum.

A)12
B)Diverges
C)3
D)16

Question 75

Select the correct Answer for each question.
Given the series estimate the error in using the partial sum by comparison with the series

A)
B)
C)
D)
E)

Question 76

Select the correct Answer for each question.
Determine which series is convergent.

A)
B)

Question 77

Select the correct Answer for each question.
Determine whether the sequence defined by converges or diverges.If it converges, find its limit.

A)13
B)5
C)Diverges
D)-3

Question 78

Select the correct Answer for each question.
Determine whether the geometric series converges or diverges.If it converges, find its sum.

A)30
B)36
C)5
D)Diverges

Question 79

Select the correct Answer for each question.
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 80

Select the correct Answer for each question.
Test the series for convergence or divergence.

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