Chapter 7: Q. 22 (page 656)
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Use either the divergence test or the integral test to determine whether the series in Given Exercises converge or diverge. Explain why the series meets the hypotheses of the test you select.
Express each of the repeating decimals in Exercises 71–78 as a geometric series and as the quotient of two integers reduced to lowest terms.
Prove Theorem 7.31. That is, show that if a function a is continuous, positive, and decreasing, and if the improper integral converges, then the nth remainder, , for the series is bounded by
Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
Use any convergence test from this section or the previous section to determine whether the series in Exercises 31–48 converge or diverge. Explain how the series meets the hypotheses of the test you select.
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