Prove-that-1-m-C-0-n-m-1-C-1-n-n-1-m-2-C-2-n-n-1-2-1-m-n-C-n-m-n-1-m-n-2-m-2n-m-n-

Question Number 23357 by Tinkutara last updated on 29/Oct/17

P r o v e t h a t \frac{1}{m!} C_{0} + \frac{n}{(m + 1)!} C_{1} + \frac{n (n - 1)}{(m + 2)!} C_{2}

+ \dots + \frac{n (n - 1) \dots 2.1}{(m + n)!} C_{n} =

\frac{(m + n + 1) (m + n + 2) \dots (m + 2 n)}{(m + n)!} .