$\displaystyle \sum_{n=3}^{\infty} \frac{2n+8}{[n ln(n)]^2 +4}$

Can anyone give me some input as to what I could compare this to. At first glance, maybe I could do a limit comparison test with

bn= $\displaystyle \frac{2n}{[n ln(n)]^2}$ , which would simplify to $\displaystyle \frac{2}{n [ln(n)]^2}$

Since n is the dominant term, would I compare it with the harmonic series of $\displaystyle \frac{1}{n}$ ??

Any feedback appreciated. Thanks.