Convergence parameter Find the values of the

Chapter 12, Problem 61E

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QUESTION:

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

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

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QUESTION:

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

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

ANSWER:

Problem 61EConvergence parameter Find the values of the parameter p for which the following series converge. SolutionStep 1In this problem we have to find the value of parameter p for which the seriesconverges.Let us use comparison test to find pComparison test:Let be positive sequences such that for all n, .1. If converges, so does 2. If diverges, so does

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