I am doing a Bayes parameter estimation in a hypergeometric distribution，and it needs the following formula： for any $x$ satisfying $0\leq x\leq n$ $$\sum_{m=0}^{N}{C_m^xC_{N-m}^{n-x}} = C_{N+1}^{n+1}$$ where $$C_n^k = \frac{n!}{k!(n-k)!}$$ $N,m,n$ are natural numbers and $n \leq N$.
I want to use $\sum_{m=0}^{N}{C_m^n} = C_{N+1}^{n+1}$ to prove this formula for it is the closest form that came in my mind, but I have no idea about the next step and whether it is the right direction.
