discrete mathematics - Prove $sum_{i=0}^nbinom{m+i}{i}=binom{m+n+1}{n}$ (another Hockey-Stick Identity?)

Let $n$ be a nonnegative integer, and $m$ a positive integer. Could someone explain to me why the identity

$$\sum_{i=0}^n\binom{m+i}{i}=\binom{m+n+1}{n}$$
holds?