Does series $sum _{n=1}^{infty :}lnleft(frac{nleft(n+2right)}{left(n+1right)^2}right)$ converge?

Does series
$\sum _{n=2}^{\infty \:}\ln\left(\frac{n\left(n+2\right)}{\left(n+1\right)^2}\right)$ converge?

My idea is to apply the Cauchy test, but I dont know how to simplify it next.

Thanks