Q: Let n,k be a positive integer, Prove that

$\displaystyle 1(C(n,1))+ 2(C(n,2)) +......+ n(C(n,n)) = n2^(n-1)$

Induction doesn't seem to work.. I have no idea what to do for this question.

Please Help.

P.S. its 2^(n-1)- dunno why it showed up like that.

Thanks,

Creative