Chapter 7: Q. 55 (page 626)
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
Chapter 7: Q. 55 (page 626)
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
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Get started for freeDetermine whether the series converges or diverges. Give the sum of the convergent series.
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.
Given a series , in general the divergence test is inconclusive when . For a geometric series, however, if the limit of the terms of the series is zero, the series converges. Explain why.
In Exercises 48–51 find all values of p so that the series converges.
Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
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