Calculus (3rd Edition)

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

Chapter 11 - Infinite Series - 11.3 Convergence of Series with Positive Terms - Exercises - Page 556: 15



Work Step by Step

Given $$\sum_{n=1}^{\infty} \frac{1}{n^{3}+8 n}$$ We compare the given series with the series $\displaystyle\sum_{n=1}^{\infty} \frac{1}{n^{3}}$ $p-$series , $p=3$ convergent and for $n\geq 1$ $$\frac{1}{n^{3}+8 n}\leq\frac{1}{n^{3}}$$ Then $\displaystyle\sum_{n=1}^{\infty} \frac{1}{n^{3}+8 n}$ also converges
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