Determining convergence or divergence

The problem asks whether this sum will converge or diverge:

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

I had:

which becomes:

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

Is it possible to simply take the limit of this or just even say that because the denominator is raised to a power of 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.