9.8 Power Series 555
9.8 Power Series
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. State where the power series is centered.
a. 0
b. –3
c. 2
d. 3
e. –2
____ 2. Find the radius of convergence of the power series.
a.
b.
c. 5
d.
e. 25
____ 3. Find the radius of convergence of the power series.
a.
b. 16
c. 64
d. 0
e. 8
556 Chapter 9: Infinite Series
____ 4. Find the interval of convergence of the power series. (Be sure to include a check for
convergence at the endpoints of the interval.)
a.
b.
c.
d.
e.
____ 5. Find the interval of convergence of the power series. (Be sure to include a check for
convergence at the endpoints of the interval.)
a.
b.
c.
d.
e.
____ 6. Find the interval of convergence of the power series. (Be sure to include a check for
convergence at the endpoints of the interval.)
a.
b.
c.
d.
e.
9.8 Power Series 557
____ 7. Find the interval of convergence of the power series. (Be sure to include a check for
convergence at the endpoints of the interval.)
a.
b.
c.
d.
e.
____ 8. Find the interval of convergence of the power series . (Be sure to
include a check for convergence at the endpoints of the interval.)
a.
b.
c.
d.
e.
____ 9. Find the interval of convergence of the power series . (Be sure to
include a check for convergence at the endpoints of the interval.)
a.
b.
c.
d.
e.
558 Chapter 9: Infinite Series
____ 10. Write an equivalent series of the series with the index of summation
beginning at .
a.
b.
c.
d.
e.
____ 11. Write an equivalent series of the series with the index of
summation beginning at .
a.
b.
c.
d.
e.
9.8 Power Series 559
____ 12. Consider the function given by . Find the interval of convergence
for .
a.
b.
c.
d.
e.
____ 13. Consider the function given by . Find the interval of convergence
for .
a.
b.
c.
d.
e.
____ 14. Consider the function given by . Find the interval of
convergence for .
a.
b.
c.
d.
e.
560 Chapter 9: Infinite Series
____ 15. Consider the function given by . Find the interval of
convergence for .
a.
b.
c.
d.
e.
____ 16. Identify the graph of the first 10 terms of the sequence of partial sum of the series
for .
a. d.
b. e.
9.8 Power Series 561
c.
____ 17. Find the differential equation having the solution .
a.
b.
c.
d.
e.
562 Chapter 9: Infinite Series
9.8 Power Series
Answer Section