Convergence of $\sum\frac{1}{n^3-n^2}$ Does this infinite series converge or diverge?
$$\sum\frac{1}{n^3-n^2} $$
I've tried every test I can think of but I can't figure it out. Is there a series greater than this that is convergent or a series smaller that is divergent? Or some other quality about this series that I am overlooking?
Please don't tell me to use the integral test, even if that method works.

$0\le \frac{1}{n^3-n^2}=\frac{1}{n^2(n-1)}<\frac {1}{n^2}$ (for all $n>10434666$).
