Chapter 7: Q. 19 (page 652)
Give an example of divergent series and such that the series role="math" localid="1649434191353" converges.
Short Answer
The seriesis convergent.
Chapter 7: Q. 19 (page 652)
Give an example of divergent series and such that the series role="math" localid="1649434191353" converges.
The seriesis convergent.
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Get started for freeFor 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.
35.
Whenever a certain ball is dropped, it always rebounds to a height p% (0 < p < 100) of its original position. What is the total distance the ball travels before coming to rest when it is dropped from a height of h meters?
Determine whether the series converges or diverges. Give the sum of the convergent series.
Explain how you could adapt the integral test to analyze a series in which the function is continuous, negative, and increasing.
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