## Calculus 10th Edition

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.