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)!)).


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

$P r o v e t h a t \frac{1}{m!} C_{0} + \frac{n}{(m + 1)!} C_{1} + \frac{n (n - 1)}{(m + 2)!} C_{2}$ $+ . . . + \frac{n (n - 1) . . . 2.1}{(m + n)!} C_{n} =$ $\frac{(m + n + 1) (m + n + 2) . . . (m + 2 n)}{(m + n)!} .$
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