Prove that:

$\displaystyle \binom{r}{k}=\frac{r}{r-k}*\binom{r-1}{k}$

Here is as far as I've gotten:

$\displaystyle r\frac{(r-1)!}{(r-1-k)!(k)!}$

which would be equal to

$\displaystyle r\binom{r-1}{r-k}$...i think

I'm stuck for the next step.

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- Apr 16th 2009, 03:07 PMchaotixmonjuishProving a binomial identity
Prove that:

$\displaystyle \binom{r}{k}=\frac{r}{r-k}*\binom{r-1}{k}$

Here is as far as I've gotten:

$\displaystyle r\frac{(r-1)!}{(r-1-k)!(k)!}$

which would be equal to

$\displaystyle r\binom{r-1}{r-k}$...i think

I'm stuck for the next step. - Apr 16th 2009, 03:46 PMTheEmptySet
- Apr 16th 2009, 03:56 PMchaotixmonjuish
Well I'm stuck as to what to factor out to get the $\displaystyle \frac{r}{r-k}$. Im not too certain at all as to how the denomenator r-k comes into play.