Answer
3
Work Step by Step
We see, from the question 20 of this exercise, that
$\Sigma^{n=\infty}_{n=1} \frac{1}{n(n+2)}=\frac {1}{2} \times\frac{3}{2} = \frac{3}{4}$
Therefore, $\Sigma^{n=\infty}_{n=1} \frac{4}{n(n+2)}= 4\times\frac{3}{4}=3$