The problem asks whether this sum will converge or diverge:

$\displaystyle \sum_{n=1}^{\infty} \frac {n(n+1)} {\sqrt {n^3+2n^2)}}$

What I had done from this point was to attempt to simplify the sum, by factoring the denominator so that instead of having:

$\displaystyle \sqrt {n^3+2n^2)}$

I had:

$\displaystyle \sqrt {n^2(n+2)}$ which becomes: $\displaystyle n\sqrt {(n+2)}$

So then back to the initial fraction, the factor of n would cancel and what would be left is:

$\displaystyle \frac {(n+1)} {\sqrt {n+2)}}$

Is it possible to simply take the limit of this or just even say that because the denominator is raised to a power of $\displaystyle \frac {1} {2}$ that the series must diverge? I am tempted to simply just note the power value and say that the sum must diverge then.

Thanks for the help, it's much appreciated.