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Math Help - Identity using Choose numbers

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    Identity using Choose numbers

    Prove this identity:
    \sum_{k=0}^{n} {n}\choose{k} = {2n}\choose{n}
    Thanks
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  2. #2
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    Quote Originally Posted by tbyou87 View Post
    Prove this identity:
    \sum_{k=0}^{n} {n}\choose{k} = {2n}\choose{n}
    Thanks
    By expanding (1 + 1)^n using the binomial theorem it's simple to show that \sum_{k=0}^{n} {n}\choose{k} = 2^n.


    So you need to prove that {2n}\choose{n} = 2^n ......
    Last edited by mr fantastic; January 29th 2008 at 07:08 PM. Reason: Fixed up the latex
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