Answer
Diverges by the n-th term test
Work Step by Step
Rewrite, $\Sigma^{\infty}_{n=1} (-1)^n \frac{n}{\ln(n+1)}$
Apply n-th term test
$\lim\limits_{n \to \infty} \frac{n}{\ln(n+1)} = \infty \ne 0$
Diverges by the n-th term test
Calculus 10th Edition
by Larson, Ron; Edwards, Bruce H.
Published by
Brooks Cole
ISBN 10:
1-28505-709-0
ISBN 13:
978-1-28505-709-5
Chapter 9 - Infinite Series - 9.5 Exercises - Page 625: 11
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