## University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson

# Chapter 9 - Section 9.4 - Comparison Tests - Exercises - Page 509: 15

Diverges

#### Work Step by Step

Consider $a_n=\dfrac{1}{\ln n}$ and $b_n=\dfrac{1}{n}$ Now, $\lim\limits_{n \to \infty}\dfrac{a_n}{b_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{1}{\ln n}}{\dfrac{1}{n}}$ Thus, we have $=\lim\limits_{n \to \infty} \dfrac{n}{\ln n}$ or, $=\infty$ Hence, the series is divergent due to the limit comparison test.

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