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9.6 The Ratio and Root Test 541
9.6 The Ratio and Root Test
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 1. Use the Ratio Test to determine the convergence or divergence of the series .
a.
b.
____ 2. Use the Ratio Test to determine the convergence or divergence of the series.
a. diverges
b. Ratio Test inconclusive
c. converges
____ 3. Use the Ratio Test to determine the convergence or divergence of the series.
a. converges
b. diverges
c.
____ 4. Use the Ratio Test to determine the convergence or divergence of the series.
a. diverges
b. converges
c. Ratio Test inconclusive
542 Chapter 9: Infinite Series
____ 5. Use the Ratio Test to determine the convergence or divergence of the series
.
a.
b.
____ 6. Use the Root Test to determine the convergence or divergence of the series .
a.
b.
____ 7. Use the Root Test to determine the convergence or divergence of the series.
a. converges
b. diverges
c. Root Test inconclusive
____ 8. Use the Root Test to determine the convergence or divergence of the series.
a. converges
b. diverges
c. Root Test inconclusive
____ 9. Use the Root Test to determine the convergence or divergence of the series.
a. Root Test inconclusive
b. converges
c. diverges
9.6 The Ratio and Root Test 543
____ 10. Use the Root Test to determine the convergence or divergence of the series .
a. converges
b. diverges
____ 11. Determine the convergence or divergence of the series using any
appropriate test.
a.
b.
____ 12. Identify the most appropriate test to be used to determine whether the series
converges or diverges.
a.
b.
c.
d.
e.
____ 13. Determine the convergence or divergence of the series using any appropriate test
from this chapter. Identify the test used.
a.
b.
c.
d.
e.
____ 14. Determine the convergence or divergence of the series using any appropriate test
from this chapter. Identify the test used.
a. converges; Ratio Test
b. both civerges; p-series and civerges; Integral Test
c. civerges; p-series
d. civerges; Integral Test
e. converges; p-series
544 Chapter 9: Infinite Series
____ 15. Determine the convergence or divergence of the series using any appropriate test
from this chapter. Identify the test used.
a. both diverges; Ratio Test and diverges; Theorem 9.9 (nth Term Test for Divergence)
b. converges; Integral Test
c. diverges; Theorem 9.9 (nth Term Test for Divergence)
d. converges; p-series
e. diverges; Ratio Test
____ 16. Determine the convergence or divergence of the series using any
appropriate test.
a.
b.
____ 17. Identify the most appropriate test to be used to determine whether the series
converges or diverges.
a.
b.
c.
d.
e.
____ 18. Determine the convergence or divergence of the series using any
appropriate test.
a.
b.
9.6 The Ratio and Root Test 545
____ 19. Identify the most appropriate test to be used to determine whether the series
converges or diverges.
a.
b.
c.
d.
e.
____ 20. The terms of a series are defined recursively. Determine the convergence or
divergence of the series. Explain your reasoning.
a. converges; Ratio Test
b. diverges; Ratio Test
c. diverges; Integral Test
d. converges; Alternating Series Test
e. converges; Root Test
____ 21. Find the values of x for which the series converges.
a.
b.
c.
d.
e.
____ 22. Find the values of x for which the series converges.
a.
b.
c.
d.
e.
546 Chapter 9: Infinite Series
9.6 The Ratio and Root Test
Answer Section
