$f(m)=\sum^m_{j=1}(m-j)2^{j-1}$ I've to understand what is a simple form of $f$ by computing some value of it, but I can't see a simple form of it, can anyone help me? I have also to give a combinatorally and inductive proof of the equality; with the inductive I think I won't have problems, but I'm not so good with the combinatorally proof, can any of you help me, please?
ok I got it, $f(m)=2^m-m-1$. Now I have to count the elements of a certain set in 2 ways to prove the equality, but I don't have any idea.