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Math Help - Proving a binomial identity

  1. #1
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    Proving a binomial identity

    Prove that:

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

    Here is as far as I've gotten:

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

    which would be equal to
    r\binom{r-1}{r-k}...i think
    I'm stuck for the next step.
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by chaotixmonjuish View Post
    Prove that:

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

    Here is as far as I've gotten:

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

    which would be equal to
    r\binom{r-1}{r-k}...i think
    I'm stuck for the next step.
    So

    \binom{r-1}{k}=\frac{(r-1)!}{k!(r-1-k)!}

    Now if we multiply by

    \frac{(r-1)!}{k!(r-1-k)!}\cdot \frac{r}{(r-k)}=\frac{r!}{k!(r-k)!}=\binom{r}{k}
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  3. #3
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    Well I'm stuck as to what to factor out to get the \frac{r}{r-k}. Im not too certain at all as to how the denomenator r-k comes into play.
    Last edited by chaotixmonjuish; April 16th 2009 at 04:22 PM.
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