Chapter 7: Q. 27 (page 615)
In Exercises 21–28 provide the first five terms of the series.
Short Answer
Ans: The five terms of the series are
Chapter 7: Q. 27 (page 615)
In Exercises 21–28 provide the first five terms of the series.
Ans: The five terms of the series are
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Get started for freeProve Theorem 7.31. That is, show that if a function a is continuous, positive, and decreasing, and if the improper integral converges, then the nth remainder, , for the series is bounded by
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 localid="1649224052075" .
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.
In Exercises 48–51 find all values of p so that the series converges.
Examples: Construct examples of the thing(s) described in the following. Try to find examples that are different than any in the reading.
(a) A divergent series in which .
(b) A divergent p-series.
(c) A convergent p-series.
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