Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 9 - Infinite Series - 9.2 Exercises: 9

Answer

By Th.9.9, the series diverges.

Work Step by Step

Th. 9.9, nth-Term Test for Divergence: If $\displaystyle \lim_{n\rightarrow\infty}a_{n}\neq 0$, then $\displaystyle \sum_{n=1}^{\infty}a_{n}$ diverges. -------------- $a_{n}=\displaystyle \frac{n}{n+1}$ and $\displaystyle \lim_{n\rightarrow\infty}\frac{n}{n+1}=1\neq 0$ By Th.9.9, the series diverges.
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