Answer
Converges
Work Step by Step
Let $u_n=\dfrac{10n+1}{n(n+1) (n+2)}$ and $v_n=\dfrac{1}{ n^2}$
Now, $\lim\limits_{n \to \infty}\dfrac{u_n}{v_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{10n+1}{n(n+1) (n+2)}}{1/ n^2}$
$\implies \lim\limits_{n \to \infty} \dfrac{10n^2+n}{(n+1)(n+2)}=\lim\limits_{n \to \infty} \dfrac{10+1/n}{(1/n+1/n^2)(1/n+2/n^2)}=10$
Thus, the series converges by the limit comparison test.