Nevermind! Listen to tonio.
That's the sum . Let's try now to understand the quotient in that infinite series a little better:
. There's a reason why we wrote the last mess:
We know (hopefully!) that , with convergence radius . Well, derivate both sides of this and get:
, and now input , do a little algebra and get your result.
Ps. This is, imho, a problem that fits the Challenge Problems Section!