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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
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Solution: Convergence parameter Find the values of the

Chapter 12, Problem 59E

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QUESTION:

58-65. Convergence parameter Find the values of the parameter p for which the following series converge.

\(\sum_{k=2}^{\infty} \frac{\ln k}{k^{p}}\)

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QUESTION:

58-65. Convergence parameter Find the values of the parameter p for which the following series converge.

\(\sum_{k=2}^{\infty} \frac{\ln k}{k^{p}}\)

ANSWER:

Problem 59EConvergence parameter Find the values of the parameter p for which the following series converge. Answer; Step 1; In this problem we have to find the value of parameter p for which the seriesconverges.Let us use integral test to find p . INTEGRAL TEST DEFINITION; Suppose f is continuous , positive , decreasing function on[1, ) , and let = f(n) . Then the convergence or divergence of the series Is the same as that of the integral f(x) dx .1. If f(x) dx is convergent , then is convergent .2. If f(x) dx is divergent , then is divergent . That is bothand converge or diverge together.

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