Answer
Converges
Work Step by Step
Consider $a_n=\dfrac{10n+1}{n(n+1) (n+2)}$ and $b_n=\dfrac{1}{ n^2}$
Now, $\lim\limits_{n \to \infty}\dfrac{a_n}{b_n} =\lim\limits_{n \to \infty}\dfrac{\dfrac{10n+1}{n(n+1) (n+2)}}{\dfrac{1}{ n^2}}$
Thus, we have $ =\lim\limits_{n \to \infty} \dfrac{10n^2+n}{(n+1)(n+2)}$
or, $=10$
Hence, the series converges due to the limit comparison test.
