Closed Form of an Infinite Series

[Frillth]

Homework Statement

I'm looking to find a closed form for the infinite series:
1*C(n,1) + 2*C(n,2) + 3*C(n,3) + ... + n*C(n,n)

Homework Equations

C(n,k) = n!/(k!*(n-k)!)
C(n,1) + C(n,2) + C(n,3) + ... + C(n,n) = 2^n - 1

The Attempt at a Solution

I'm not quite sure where to start this problem. Any tips?

 

[Dick]

(1+x)^n=C(0,n)+C(1,n)*x+C(2,n)*x^2+...+C(n,n)*x^n. This is why it's clear that your second identity is pretty obvious (put x=1). Think what happens when you differentiate that wrt x and then put x=1. Oh, and your series really isn't that infinite, is it?