Answer
Diverges
Work Step by Step
When $x$ approaches $0$, $\ln x$ always tends to $-\infty$ and $\dfrac{1}{n} \to 0$ as $n \to \infty$
Therefore, $\lim\limits_{n \to \infty} \ln \dfrac{1}{n}=-\infty\ne 0$
Hence, the series is divergent.
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 497: 33
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