value of summation of $2^i\cdot i$ I'm trying to calculate the value of 
$$2^0\cdot0 + 2^1\cdot1 + 2^2\cdot2 + .... 2^n\cdot n$$
I figured this would be summation $2^i \cdot i$ from $i = 0$ to $n$. But iI'm unable to calculate its value.  
I have tried searching online but haven't been able to find a formula or any property that 
could simplify it (maybe there was which I might not have understood)
P.S.This is not a homework question, I need this value to prove a theorem.

Hint: Note that $nx^n=x(x^n)'$, so your series is the derivative of a geometric series evaluated at $x=2$.
