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Chapter 7: Q. 11 (page 656)
Geometric Series and p-series:
Suppose r is a nonzero real number and p > 0. Fill in the blanks.
For r_____, the geometric series diverges.
The required answer is forthe geometric seriesdiverges.
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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.
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.
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.
36.
Let Prove that the series diverges.
Use the divergence test to analyze the given series. Each answer should either be the series diverges or the divergence test fails, along with the reason for your answer.
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