Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - Chapter Review Exercises - Page 592: 83


The series $\sum_{n=2}^{\infty} \frac{(-1)^{n}}{ \ln n}$ converges.

Work Step by Step

The positive, decreasing term is $b_n=\frac{1}{\ln n}$; now we have $$\lim_{n\to \infty } b_n=\lim_{n\to \infty } \frac{1}{\ln n}=\frac{1}{\infty}=0.$$ Hence, using the alternating series test, the series $\sum_{n=2}^{\infty} \frac{(-1)^{n}}{ \ln n}$ converges.
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