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Chapter 7: Q. 24 (page 652)
Use the alternating series test to determine whether the series in Exercises 24鈥29 converge or diverge. If a series converges, determine whether it converges absolutely or conditionally.
The seriesdiverges
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Prove that if converges to L and converges to M , then the series.
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.
Determine whether the series converges or diverges. Give the sum of the convergent series.
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" .
Let be a continuous, positive, and decreasing function. Complete the proof of the integral test (Theorem 7.28) by showing that if the improper integral converges, then the series localid="1649180069308" does too.
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