Deck 9: Infinite Series

Question 1

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

A)
B)
C)
D)
E)

Answer 1

Question 2

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

A)
B)
C)
D)
E)

Answer 2

Question 3

True or false.The series is divergent.

Answer 3

True

Question 4

True or false.The infinite series

Question 5

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 6

Find the sum of the convergent series

A)
B)
C)
D)
E)

Question 7

Find the sum of the convergent series.

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

Question 8

Determine the convergence or divergence of the series.

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

Question 9

Write the repeating decimal as a geometric series.

A)
B)
C)
D)
E)

Question 10

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 11

Find all values of x for which the series converges.

A)
B)
C)
D)
E)

Question 12

Find the sum of the convergent series.

A)
B)
C)
D)
E)

Question 13

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

A)
B)
C)
D)
E)

Question 14

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

Question 15

Find all values of x for which the series converges.For these values of x, write the sum of the series as a function of x.

A)
B)
C)
D)
E)The series diverges for all x.

Question 16

Find the sum of the convergent series.

A)
B)
C)
D)
E)

Question 17

Find the sum of the convergent series

A)
B)
C)
D)
E)

Question 18

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 19

True or false.The series is convergent.

Question 20

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 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