536 Chapter 9: Infinite Series
9.5 Alternating Series
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. True or false: The series converges.
a.
b.
____ 2. True or false: The series diverges.
a.
b.
____ 3. True or false: The series converges.
a.
b.
____ 4. True or false: The series converges .
a.
b.
____ 5. Determine whether the series converges conditionally or absolutely, or
diverges.
a. The series converges conditionally but does not converge absolutely.
b. The series converges absolutely but does not converge conditionally.
c. The series diverges.
d. The series converges absolutely.
9.5 Alternating Series 537
____ 6. Determine whether the series converges absolutely, converges
conditionally, or diverges.
a.
b. diverges
c.
____ 7. Determine whether the series converges conditionally or absolutely, or
diverges.
a. The series converges absolutely.
b. The series diverges.
c. The series converges absolutely but does not converge conditionally.
d. The series converges conditionally but does not converge absolutely.
____ 8. Determine whether the series converges conditionally or absolutely,
or diverges.
a. The series converges absolutely.
b. The series diverges.
c. The series converges absolutely but does not converge conditionally.
d. The series converges conditionally but does not converge absolutely.
____ 9. Approximate the sum of the series by using the first six terms.
a. 1.457 < S < 1.477
b. 1.417 < S < 1.497
c. 1.467 < S < 1.472
d. 1.427 < S < 1.467
e. 1.461 < S < 1.473
____ 10. Approximate the sum of the series by using the first six terms.
a. 1.799 < S < 1.805
b. 1.794 < S < 1.806
c. 1.794 < S < 1.805
d. 1.792 < S < 1.792
e. 1.698 < S < 1.902
538 Chapter 9: Infinite Series
____ 11. Determine the minimal number of terms required to approximate the sum of the
series with an error of less than 0.007.
a. 5
b. 4
c. 2
d. 6
e. 3
____ 12. Determine the minimal number of terms required to approximate the sum of the
series with an error of less than 0.004.
a. 10
b. 5
c. 8
d. 6
e. 4
____ 13. Determine the minimal number of terms required to approximate the sum of the
series with an error of less than 0.008.
a. 3
b. 1
c. 4
d. 6
e. 2
____ 14. Determine the minimal number of terms required to approximate the sum of the
series with an error of less than 0.005.
a. 6
b. 4
c. 5
d. 8
e. 3
9.5 Alternating Series 539
____ 15. Approximate the sum of the series by using the first six terms.
a. 0.587 < S < 3.473
b. 1.549 < S < 2.511
c. 1.309 < S < 2.751
d. 0.427 < S < 3.633
e. 0.227 < S < 3.833
540 Chapter 9: Infinite Series
9.5 Alternating Series
Answer Section