Answer
$\frac{3}{2}$
Work Step by Step
$\Sigma \frac{2}{n^2-1}=\Sigma (\frac{1}{n-1}-\frac{1}{n+1})$
$=(\frac{1}{1}-\frac{1}{3})+(\frac{1}{2}-\frac{1}{4})+(\frac{1}{3}-\frac{1}{5})+(\frac{1}{4}-\frac{1}{6})+...=\frac{1}{1}+\frac{1}{2}=\frac{3}{2}$
