Umm, unfortunately , not 0, as .

I haven't been able to think of any way of attacking this problem. It's clear that as , but it approaches 0 so desperately slowly that I very much doubt whether converges. Maybe the series of p'th powers will converge if p is large enough, but I don't see why even that should hold.

It's a very interesting problem! I hope someone can find a way to tackle it.