Determine whether the follwing series is convergent or divergent. If it is convergent, find the sum. $$\sum\limits_{n=1}^\infty\frac{1}{n^2+5n+6}$$
Here's my work so far:
$\lim_\limits{n\to\infty}\frac{1}{n^2+5n+6} = 0$
$\therefore\;$ the series is convergent.
I don't think it's a geometric series since there is no common factor between the consecutive terms. Because it isn't a geometric series, I'm at a loss as to what formula to use.