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.
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$a_{n}=\displaystyle \frac{n}{n+1}$
and
$\displaystyle \lim_{n\rightarrow\infty}\frac{n}{n+1}=1\neq 0$
By Th.9.9, the series diverges.
