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Chapter 7: Q. 11 (page 603)
Give examples of sequences satisfying the given conditions or explain why such an example cannot exist.
Two convergent sequencessuch that the sequencediverges.
Examples satisfying the given conditions is .
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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.
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 localid="1649224052075" .
Express each of the repeating decimals in Exercises 71鈥�78 as a geometric series and as the quotient of two integers reduced to lowest terms.
Use either the divergence test or the integral test to determine whether the series in Exercises 32鈥�43 converge or diverge. Explain why the series meets the hypotheses of the test you select.
36.
Letand be two convergent geometric series. If b and v are both nonzero, prove that is a geometric series. What condition(s) must be met for this series to converge?
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