University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.2 - Infinite Series - Exercises - Page 497: 33

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.
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