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Chapter 7: Q. 38 (page 615)
Evaluate the finite sums.
The sum of the seriesis,.
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Whenever a certain ball is dropped, it always rebounds to a height60% of its original position. What is the total distance the ball travels before coming to rest when it is dropped from a height of 1 meter?
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.
35.
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.
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.
Let f(x) be a function that is continuous, positive, and decreasing on the interval such that role="math" localid="1649081384626" . What can the divergence test tell us about the series ?
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