   Chapter 11.4, Problem 9E

Chapter
Section
Textbook Problem

# Determine whether the series converges or diverges.9. ∑ k = 1 ∞ ln k k

To determine

Whether the series k=1lnkk converges or diverges.

Explanation

Given:

The series is k=1lnkk .

Result used:

(1) “Suppose that an and bn are the series with positive terms,

(a) If bn is convergent and anbn for all n , then an is also convergent.

(b) If bn is divergent and anbn for all n , then an is also divergent.”

(2) The p-series is convergent if p>1 and diverges if p1 .

Calculation:

Consider the given series k=1lnkk

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