516 Chapter 9: Infinite Series
9.2 Series and Convergence
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Write the first five terms of the sequence of partial sums.
a.
b.
c.
d.
e.
____ 2. Write the first five terms of the sequence of partial sums.
a.
b.
c.
d.
e.
9.2 Series and Convergence 517
____ 3. Write the first five terms of the sequence of partial sums.
a.
b.
c.
d.
e.
____ 4. True or false. The infinite series .
a. false
b. true
____ 5. Find the sum of the convergent series.
a. 4
b. 36
c. 9
d. 27
e. 45
____ 6. Find the sum of the convergent series.
a.
518 Chapter 9: Infinite Series
b.
c.
d.
e.
____ 7. Find the sum of the convergent series.
a.
b.
c.
d.
e.
____ 8. Find the sum of the convergent series
a.
b.
c.
d.
e.
9.2 Series and Convergence 519
____ 9. Find the sum of the convergent series .
a.
b.
c.
d.
e.
____ 10. Write the repeating decimal as a geometric series.
a.
b.
c.
d.
e.
520 Chapter 9: Infinite Series
____ 11. True or false. The series is convergent.
a. false
b. true
____ 12. True or false. The series is divergent.
a. false
b. true
____ 13. Determine the convergence or divergence of the series.
a. cannot be determined from the methods in the chapter
b. Diverges
c. Converges
____ 14. Find all values of x for which the series converges.
a.
b.
c.
d.
e.
____ 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.
9.2 Series and Convergence 521
d.
e. The series diverges for all x.
____ 16. 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
____ 17. 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
____ 18. 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
522 Chapter 9: Infinite Series
____ 19. 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
____ 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
____ 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
9.2 Series and Convergence 523
9.2 Series and Convergence
Answer Section