Deck 9: Section 2: Infinite Series

Question 1

True or false. The infinite series .

A) false
B) true

Answer 1

true

Question 2

Write the first five terms of the sequence of partial sums.

A)
B)
C)
D)
E)

Answer 2

Question 3

Write the repeating decimal as a geometric series.

A)
B)
C)
D)
E)

Answer 3

Question 4

Determine the convergence or divergence of the series.

A) cannot be determined from the methods in the chapter
B) Diverges
C) Converges

Question 5

Match the series with the graph of its sequence of partial sums.

A)
B)
C)
D)
E)

Question 6

Match the series with the graph of its sequence of partial sums.

A)
B)
C)
D)
E)

Question 7

Write the first five terms of the sequence of partial sums.

A)
B)
C)
D)
E)

Question 8

True or false. The series is divergent.

A) false
B) true

Question 9

Find the sum of the convergent series.

A) 4
B) 36
C) 9
D) 27
E) 45

Question 10

Match the series with the graph of its sequence of partial sums.

A)
B)
C)
D)
E)

Question 11

Suppose an electronic games manufacturer producing a new product estimates the annual sales to be 4,000 units. Each year 20% of the units that have been sold will become inoperative. So, 4,000 units will be in use after 1 year, units will be in use after 2 years, and so on. How many units will be in use after n years?

A) units
B) units
C) units
D) units
E) units

Question 12

Find all values of x for which the series converges.

A)
B)
C)
D)
E)

Question 13

Suppose the annual spending by tourists in a resort city is $100 million. Approximately 75% of that revenue is again spent in the resort city, and of that amount approximately 75% is again spent in the same city, and so on. Summing all of this spending indefinitely, leads to the geometric series . Find the sum of this series.

A) $800 million
B) $401 million
C) $200 million
D) $801 million
E) $400 million

Question 14

Find the sum of the convergent series .

A)
B)
C)
D)
E)

Question 15

True or false. The series is convergent.

A) false
B) true

Question 16

Find the sum of the convergent series

A)
B)
C)
D)
E)

Question 17

Write the first five terms of the sequence of partial sums.

A)
B)
C)
D)
E)

Question 18

Find the sum of the convergent series.

A)
B)
C)
D)
E)

Question 19

Suppose the annual spending by tourists in a resort city is $100 million. Approximately 90% of that revenue is again spent in the resort city, and of that amount approximately 90% is again spent in the same city, and so on. Write the expression that gives the total amount of spending generated by the $100 million after n years.

A) million dollars
B) million dollars
C) million dollars
D) million dollars
E) million dollars

Question 20

Find the sum of the convergent series.

A)
B)
C)
D)
E)

Question 21

Suppose you go to work at a company that pays $0.08 for the first day, $0.16 for the second day, $0.32 for the third day, and so on. If the daily wage keeps doubling, what would your total income be for working 29 days? Round your answer to two decimal places.

A) $21,474,836.48
B) $10,737,418.24
C) $42,949,672.88
D) $171,798,691.52
E) $85,899,345.76

Question 22

Suppose the winner of a $4,000,000 sweepstakes will be paid $100,000 per year for 40 years, starting a year from now. The money earns 5% interest per year. The present value of the winnings is Compute the present value using the formula for the nth partial sum of a geometric series. Round your answer to two decimal places.

A) $6,852,274.09
B) $1,959,646.05
C) $4,568,182.73
D) $1,246,221.03
E) $1,715,908.64

Question 23

Suppose a ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.85h feet. Find the total distance traveled by the ball. Round your answer to two decimal places.

A) 229.33 feet
B) 410.67 feet
C) 181.33 feet
D) 197.33 feet
E) 213.33 feet