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Chapter 7: Q. 25 (page 657)
Check the convergence
Diverges.
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For each series in Exercises 44鈥�47, do each of the following:
(a) Use the integral test to show that the series converges.
(b) Use the 10th term in the sequence of partial sums to approximate the sum of the series.
(c) Use Theorem 7.31 to find a bound on the tenth remainder,.
(d) Use your answers from parts (b) and (c) to find an interval containing the sum of the series.
(e) Find the smallest value of n so that
Ifconverges, explain why we cannot draw any conclusions about the behavior of.
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.
Find an example of a continuous function f :such that diverges and localid="1649077247585" converges.
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.
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