Prove-that-n-C-r-n-C-r-1-n-1-C-r-1-

Question Number 32977 by Mr eaay last updated on 08/Apr/18

P r o v e t h a t^{n} C_{r} +^{n} C_{r + 1} =^{n + 1} C_{r + 1}

Answered by math1967 last updated on 08/Apr/18

n! {\frac{1}{r! (n - r)!} + \frac{1}{(n - r - 1)! (r + 1)!}}

\frac{n!}{(n - r - 1)! r!} {\frac{1}{n - r} + \frac{1}{r + 1}}

\frac{n! (n + 1)}{(n - r - 1)! (n - r) (r)! (r + 1)}

\frac{(n + 1)!}{(n - r)! (r + 1)!} = \frac{(n + 1)!}{(n + 1 - r - 1)! (r + 1)!}

{\overset{n + 1}{C}}_{r + 1}

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