Deck 10: Infinite Series

Question 1

Determine whether the sequence converges or diverges.

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

Answer 1

converges to 0

Question 2

Write out terms of the given sequence.

Answer 2

, ,

Question 3

Find the limit of the sequence .

A) 0
B) 8
C)
D) does not exist

Answer 3

0

Question 4

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

A)
B)
C)
D)

Question 5

Write out terms of the given sequence.

Question 6

Show that is bounded. Show all your work.

Question 7

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

A) 9
B)
C)
D) diverges

Question 8

Determine whether is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither

Question 9

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 10

Find the limit of the sequence.

A) 1
B)
C) 7
D) 2

Question 11

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 12

Find the limit of the sequence .

A) -4
B) 0
C) 4
D) does not exist

Question 13

Determine whether the sequence converges or diverges.

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

Question 14

Determine whether converges or diverges. Show all your work.

Question 15

Determine whether is increasing, decreasing or neither.

A) decreasing
B) increasing
C) neither

Question 16

Determine whether converges or diverges. Show all your work.

Question 17

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

A)
B)
C)
D)

Question 18

Determine whether converges or diverges. Show all your work.

Question 19

Show that is bounded. Show all your work.

Question 20

Evaluate the limit.

A) 10
B) 0
C) 1
D) limit does not exist

Question 21

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 22

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 23

Suppose that the total salary of all the employees at a factory in a certain city is $350,000. Of this salary, 80% is spent in the city. Of the money spent in the city, 80% 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) $2,800,000
B) $504,000
C) $1,400,000
D) $683,200

Question 24

Determine convergence or divergence of the series.

Question 25

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 26

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 27

Determine convergence or divergence of the series.

Question 28

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

Question 29

Determine all values of p for which the series converges.

A)
B)
C)
D)

Question 30

A dosage of 50 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) 83 mL
B) 125 mL
C) 111 mL
D) 152 mL

Question 31

Determine all values of p for which the series converges.

A)
B)
C)
D)

Question 32

Write as a fraction.

A)
B)
C)
D)

Question 33

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

Question 34

Determine convergence or divergence of the series.

Question 35

Imagine a ball dropped from a height of 40 meters. Each time it strikes the ground, it bounces 0.68 times as high as the previous bounce. Find the total distance the ball will travel if it is allowed to bounce indefinitely.

A) 27.2 meters
B) 0.32 meters
C) 210 meters
D) 40 meters

Question 36

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 37

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

Question 38

Determine convergence or divergence of the series.

Question 39

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

Question 40

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

Question 41

Determine whether the series is convergent or divergent.

Question 42

Estimate the sum of to within 0.01.

A) 0.10
B) 2.00
C) 1.97
D) 0.03

Question 43

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

A) k = 8000
B) k = 13
C) k = 89
D) k = 5

Question 44

Determine if converges or diverges. Show your work.

Question 45

Estimate the sum of to within 0.01.

A) 3.84
B) 3.75
C) 3.79
D) -0.25

Question 46

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 47

Determine whether the series is convergent or divergent.

Question 48

Determine if converges or diverges. Show your work.

Question 49

Determine if converges or diverges. Show your work.

Question 50

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 51

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

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 52

Estimate the sum of to within 0.01.

A) -0.12
B) -0.16
C) -0.09
D) -0.01

Question 53

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

A) k = 30
B) k = 31
C) k = 9
D) k = 0.9999

Question 54

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

Question 55

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

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 56

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

A) k = 5
B) k = 6
C) k = 5,000
D) k = 50,000

Question 57

Determine whether the series is convergent or divergent.

Question 58

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 59

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

A) 20
B) 55
C) 209
D) 2,250,001

Question 60

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

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 61

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 62

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

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

Question 63

Determine the radius and interval of convergence.

A)
B)
C)
D) converges for

Question 64

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 65

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

A)
B)
C)
D)

Question 66

Determine the radius and interval of convergence of .

A)
B)
C)
D)

Question 67

Determine the radius and interval of convergence of .

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)

Question 70

Determine if is absolutely convergent, conditionally convergent or divergent.

A) absolutely convergent
B) conditionally convergent
C) divergent

Question 71

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

A)
B)
C)
D)

Question 72

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

Question 73

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

A)
B)
C)
D)

Question 74

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

A)
B)
C)
D)

Question 75

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

A)
B)
C)
D)

Question 76

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

A)
B)
C)
D)

Question 77

Determine the radius and interval of convergence.

A)
B)
C)
D)

Question 78

Find the MacLaurin series and its interval of convergence.

A)
B)
C)
D)

Question 79

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

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

Question 80

Determine the radius and interval of convergence of .

A)
B)
C)
D)