Chapter 7: Q. 26 (page 639)
Simplify the quotients in Exercises 21–28 without using a calculator.
The value is
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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.
For a convergent series satisfying the conditions of the integral test, why is every remainder positive? How can be used along with the term from the sequence of partial sums to understand the quality of the approximation ?
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.
Let 0 < p < 1. Evaluate the limit
Explain why we cannot use a p-series with 0 < p < 1 in a limit comparison test to verify the divergence of the series
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