trying to find divergence or convergence of:

the series from n=2 to infinity of (1)/((n^p)-(n^q)) (0<q<p) using limit comparison test

Using limit comparison I have

i used 1/n^p

used reciprical and multiplied by original

(1)/((n^p)-(n^q)) x (n^p/1)

simplified and ended up with this and cannot figure out what to do or if it is even right

(1)/(1-(1/n^p)) found the limit to be 1 then is it divergent by nth term test?