NEED CALC HELP! (PLEASE!!!)

Have you heard of squeeze theorem? That's where -1<=cosx<=1, as x --> 0. So if we take x^n * cos(nx), and put it into squeeze theorem, we can get it to approach a particular point. So:
Let y=nx
-1<=cosy<=1
-x^n<=x^n * cosy<=x^n
and when x --> 0, (I've also substituted y=nx back in)
-0^n<=x^n * cosnx<=0^n
0<=x^n * cosnx<=0
so x^n * cosnx converges to zero. If you add the sums, it's still zero.

I don't know if there's more, but you can try to play with the squeeze theorem. The point is, graphically speaking, you want to get the cosine function to force the wave to approach a particular point, instead of oscillating between -1 and 1. I don't particularly remember much about series, but you could try to use squeeze theorem.