Answer
Diverges
Work Step by Step
Consider $a_n=\dfrac{(n-1)!}{(n+1)^2}$
Now, $l=\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_{n+1}} |=\lim\limits_{n \to \infty}|\dfrac{\dfrac{(n)!}{(n+2)^2}}{\dfrac{(n-1)!}{(n+1)^2}}|$
Thus, we have $l=\lim\limits_{n \to \infty}|\dfrac{n(n+1)^2}{(n+2)^2}|=\lim\limits_{n \to \infty}|\dfrac{n^3+n+2n^2}{n^2+4+4n}|=\lim\limits_{n \to \infty}|\dfrac{1+1/n^2+2/n}{1/n+4/n^3+4/n^2}|=\infty$
Hence, the series Diverges by the ratio test.