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Chapter 7: Q. 10 (page 652)
What condition(s) must a series satisfy in order for the series to be conditionally convergent?
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Determine whether the series converges or diverges. Give the sum of the convergent series.
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.
For each series in Exercises 44–47, 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.
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
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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