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 591: 43


By the comparison test, the series $\sum_{n=1}^{\infty}\frac{1}{(1+n)^2}$ coverges.

Work Step by Step

The p-series $\sum_{n=1}^{\infty}\frac{1}{n^2}$ converges and we have $$\frac{1}{1+n}\leq\frac{1}{n}\Longrightarrow \frac{1}{(1+n)^2}\leq\frac{1}{n^2} $$ Then by the comparison test, the series $\sum_{n=1}^{\infty}\frac{1}{(1+n)^2}$ converges.
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