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