Answer
Converges by Telescoping Series
Work Step by Step
$\Sigma^{\infty}_{n=1} (\frac{1}{n+1} - \frac{1}{n+2}) $
Write a few terms in the series
$(\frac{1}{2} - \frac{1}{3}) + (\frac{1}{3} - \frac{1}{4}) + (\frac{1}{4} - \frac{1}{5}) +... + ( - \frac{1}{n+2}) $
Because all the terms cancel except for the first and last, find the limit as they go to infinity
$\lim\limits_{n \to \infty} \frac{1}{2} - \frac{1}{n+2} = \frac{1}{2}$
Converges by Telescoping Series
