show-that-n-c-r-1-n-c-r-n-1-c-r-1-

Question Number 66262 by peter frank last updated on 11/Aug/19

s h o w t h a t

^{n} c_{r + 1} +^{n} c_{r} =^{n + 1} c_{r + 1}

Commented by mathmax by abdo last updated on 12/Aug/19

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

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

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

= C_{n + 1}^{r + 1}

Commented by peter frank last updated on 12/Aug/19

t h a n k y o u

Commented by mathmax by abdo last updated on 12/Aug/19

y o u a r e w e l c o m e .