Answer
It converges by the Limit Comparison Test
Work Step by Step
It converges by the Limit Comparison Test Since
$\lim\limits_{n \to \infty}\frac{\frac{a_{n}}{1+a_{n}}}{a_{n}}=\lim\limits_{n \to \infty}\frac{1}{1+a_{n}}=1$
because $\Sigma$ $a_{n}$ converges and so $a_{n} -> 0$
