\begin{align*} \mu & = E[X] \\ & = \sum_{x=0}^{n} {x \binom{n}{x} p^x (1-p)^{n-x}}\\ & = \sum_{x=1}^{n} {x \frac{n(n-1)!}{x(x-1)!(n-x)!} p^x (1-p)^{n-x}}\\ & = np \sum_{x=1}^{n} {\frac{(n-1)!}{(x-1)!((n-1)-(x-1))!} p^{x-1} (1-p)^{(n-1)-(x-1)}} \end{align*}