Deck 9: Infinite Series

Question 1

Write out terms of the given sequence.

Answer 1

, ,

Question 2

Determine whether converges or diverges. Show all your work.

Answer 2

; the limit does not exist, so the sequence diverges.

Question 3

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

A) 7
B)
C)
D) diverges

Answer 3

B

Question 4

Show that is bounded. Show all your work.

Question 5

Write a formula that produces the given terms of the sequence. , ,

A)
B)
C)
D)

Question 6

Evaluate the limit.

A) 9
B) 0
C) 1
D) limit does not exist

Question 7

Determine whether is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither

Question 8

Determine whether the sequence converges or diverges.

A) converges to 0
B) converges to
C) converges to
D) diverges

Question 9

Find the limit of the sequence .

A) -7
B) 0
C) 7
D) does not exist

Question 10

Find the limit of the sequence.

A) 1
B)
C) 7
D) 5

Question 11

Determine whether converges or diverges. Show all your work.

Question 12

Determine whether the sequence converges or diverges.

A) converges to 0
B) converges to 1
C) converges to
D) diverges

Question 13

Determine whether is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither

Question 14

Show that is bounded. Show all your work.

Question 15

Write out terms of the given sequence.

Question 16

Determine if converges or diverges. If convergent, find the sum of the series.

A) converges with sum =
B) converges with sum =
C) converges with sum =
D) diverges

Question 17

Find the limit of the sequence .

A) 0
B) 9
C)
D) does not exist

Question 18

Determine if converges or diverges. If convergent, find the sum of the series.

A) converges with sum =
B) converges with sum =
C) converges with sum =
D) diverges

Question 19

Determine whether converges or diverges. Show all your work.

Question 20

Write a formula that produces the given terms of the sequence. , , ,

A)
B)
C)
D)

Question 21

Determine convergence or divergence of the series.

Question 22

Determine all values of p for which the series converges.

A)
B)
C)
D)

Question 23

Determine all values of c such that the series converges.

A) any real number
B) c in the interval
C) c in the interval
D) c in the interval

Question 24

Estimate the error in using to approximate the sum of . Show all your work.

Question 25

Determine all values of p for which the series converges.

A)
B)
C)
D)

Question 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

Question 27

Determine convergence or divergence of the series.

Question 28

Use graphical and numerical evidence to conjecture whether the series converges or diverges.

A) diverges
B) converges to 0.9
C) converges to
D) converges to

Question 29

Determine the convergence or divergence of .
Show all your work.

Question 30

Determine convergence or divergence of the series.

Question 31

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.

A) 333 mL
B) 500 mL
C) 443 mL
D) 607 mL

Question 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

Question 33

Determine convergence or divergence of the series.

Question 34

Estimate the error in using to approximate the sum of . Show all your work.

Question 35

Determine if converges or diverges. If convergent, find the sum of the series.

A) converges with sum =
B) converges with sum =
C) converges with sum =
D) diverges

Question 36

Determine the convergence or divergence of .
Show all your work.

Question 37

Determine the convergence or divergence of .
Show all your work.

Question 38

Determine if converges or diverges. If convergent, find the sum of the series.

A) converges with sum =
B) converges with sum =
C) converges with sum =
D) diverges

Question 39

Use graphical and numerical evidence to conjecture whether the series converges or diverges. .

A) converges with sum =
B) converges with sum =
C) converges with sum =
D) diverges

Question 40

Write as a fraction.

A)
B)
C)
D)

Question 41

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

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 42

Estimate the error in using to approximate the sum of . Show all your work.

Question 43

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

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 44

Determine the number of terms needed to obtain the sum of to within 10^-6.

A) 282
B) 200
C) 2,829
D) 2,666,668

Question 45

Determine whether the series is convergent or divergent.

Question 46

Determine the number of terms needed to obtain the sum of to within 10^-6.

A) or n = 13
B) or n = 2
C) or n = 4
D) or n = -13

Question 47

Determine if converges or diverges. Show your work.

Question 48

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 49

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 50

Estimate the sum of to within 0.01.

A) -0.14
B) -0.18
C) -0.11
D) -0.08

Question 51

Estimate the sum of to within 0.01.

A) 0.10
B) 5.00
C) 4.96
D) 0.04

Question 52

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

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 53

Determine whether the series is convergent or divergent.

Question 54

Estimate the sum of to within 0.01.

A) 2.58
B) 2.50
C) 2.53
D) -0.17

Question 55

Determine how many terms are needed to estimate to within 0.0001.

A) k = 7
B) k = 8
C) k = 6,999
D) k = 70,000

Question 56

Determine whether the series is convergent or divergent.

Question 57

Determine if converges or diverges. Show your work.

Question 58

Determine how many terms are needed to estimate to within 0.001.

A) k = 4000
B) k = 28
C) k = 63
D) k = 5

Question 59

Determine how many terms are needed to estimate to within 0.0001.

A) k = 26
B) k = 27
C) k = 8
D) k = 0.9997

Question 60

Determine if converges or diverges. Show your work.

Question 61

Determine the radius and interval of convergence.

A)
B)
C)
D)

Question 62

Find a power series representation and radius of convergence for by integrating or differentiating a series.

A) ;
B) ;
C) ;
D) ;

Question 63

Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.

A)
B)
C)
D)

Question 64

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 65

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 66

Find a power series representation and radius of convergence for by integrating or differentiating a series.

A) ;
B) ;
C) ;
D) ;

Question 67

Find the interval of convergence and function f(x) to which converges.

A)
B)
C)
D)

Question 68

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 69

Determine the radius and interval of convergence.

A)
B)
C)
D) converges for

Question 70

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 71

Find the interval of convergence and function f(x) to which converges.

A)
B)
C)
D)

Question 72

Find the MacLaurin series and its interval of convergence.

A)
B)
C)
D)

Question 73

Determine the radius and interval of convergence of .

A)
B)
C)
D)

Question 74

Find a power series representation of about Determine the interval of convergence for the power series.

A)
B)
C)
D)

Question 75

Determine the radius and interval of convergence of .

A)
B)
C)
D)

Question 76

Find the power series representation (about c = 0), the radius of convergence, and the interval of convergence.

A)
B)
C)
D)

Question 77

Determine the radius and interval of convergence.

A)
B)
C)
D)

Question 78

Find the interval of convergence of the (non-power) series and the corresponding series of derivatives.

A)
B)
C)
D)

Question 79

Determine the radius and interval of convergence of .

A)
B)
C)
D)

Question 80

Determine the interval of convergence and the function to which the power series converges.