Find sum of binominal formula and prove it I have hard time with finding sum of this: $$ \sum_{k=1}^{n}k{n\choose k} $$ Please help! Prferably with some good hints.

**Hint**. Recall that $\binom nk$ counts the $k$-subsets of an $n$-set. So $$ \sum_{k=1}^n k \binom nk = \left|\left\\{(A,x) : x \in A, A \subseteq \\{0,\ldots, n-1\right\\}\right| $$ Counting in another way (first choosing $x$, then the set $A$), we have $$ \sum_{k=1}^n k\binom nk = n \sum_{k=1}^{n} \binom{n-1}{k-1} $$ (and the last sum can be computed easily).