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Math Help - binomials coefficients 2

  1. #1
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    binomials coefficients 2

    Some one pls help me with this prob pls...*
    Can someone simplify this?....thanks



    <br />
N=(-1)^k(-n)(-n+1)...(-n+k-1)<br />
=(-1)^k\binom{-n+k-1}{k}k!<br />

    can we use principle of mathematical induction with this? someone help me solve this problem pls
    Last edited by mr fantastic; September 17th 2009 at 02:21 AM. Reason: Merged posts
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  2. #2
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    Work the other way around ... show that (-1)^k\binom{-n+k-1}{k}k!<br />
=(-1)^k(-n)(-n+1)...(-n+k-1)

    \binom{a}{b}=\frac{a!}{b!(a-b)!}

    So \binom{-n+k-1}{k}k!<br />
=\frac{(-n+k-1)!k!}{k!(-n+k-1-k)!}=\frac{(-n+k-1)!}{(-n-1)!}
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