Chapter 7: Q. 30 (page 625)
Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
Short Answer
Ans: The seriesis divergent.
Chapter 7: Q. 30 (page 625)
Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
Ans: The seriesis divergent.
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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
In Exercises 48–51 find all values of p so that the series converges.
Ifconverges, explain why we cannot draw any conclusions about the behavior of.
Let 0 < p < 1. Evaluate the limit
Explain why we cannot use a p-series with 0 < p < 1 in a limit comparison test to verify the divergence of the series
Explain why the integral test may be used to analyze the given series and then use the test to determine whether the series converges or diverges.
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