Answer
By the comparison test, the series $\sum_{n=1}^{\infty}\frac{1}{(1+n)^2}$ coverges.
Work Step by Step
The p-series $\sum_{n=1}^{\infty}\frac{1}{n^2}$ converges and we have
$$\frac{1}{1+n}\leq\frac{1}{n}\Longrightarrow \frac{1}{(1+n)^2}\leq\frac{1}{n^2} $$
Then by the comparison test, the series $\sum_{n=1}^{\infty}\frac{1}{(1+n)^2}$ converges.
