Prove that ^n C_r +^n C_(r+1) =^(n+1) C


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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
	$n!{(1/(r!(n−r)!)) +(1/((n−r−1)!(r+1)!))} ((n!)/((n−r−1)!r!)){(1/(n−r)) +(1/(r+1))} ((n!(n+1))/((n−r−1)!(n−r)(r)!(r+1))) (((n+1)!)/((n−r)!(r+1)!))=(((n+1)!)/((n+1−r−1)!(r+1)!)) C_(r+1) ^(n+1)$
	$n! {\frac{1}{r! (n - r)!} + \frac{1}{(n - r - 1)! (r + 1)!}}$ $\frac{n!}{(n - r - 1)! r!} {\frac{1}{n - r} + \frac{1}{r + 1}}$ $\frac{n! (n + 1)}{(n - r - 1)! (n - r) (r)! (r + 1)}$ $\frac{(n + 1)!}{(n - r)! (r + 1)!} = \frac{(n + 1)!}{(n + 1 - r - 1)! (r + 1)!}$ ${\overset{n + 1}{C}}_{r + 1}$
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