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Math Help - Proof regarding combinations

  1. #1
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    Proof regarding combinations

    Show that:

    (n choose 1) + (n choose 3) + ... = (n choose 0) + (n choose 2) + ...

    I understand that the left side is all of the odd sized combinations from a set of n distinct objects and the right side is all of the even sized combinations from a set of n distinct objects, but I'm not exactly sure how to go about proving this.

    Thanks.
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  2. #2
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    Quote Originally Posted by donald17 View Post
    Show that:
    (n choose 1) + (n choose 3) + ... = (n choose 0) + (n choose 2) + ...
    \left( {x + y} \right)^n  = \sum\limits_{j=0}^{n} {\binom{n}{j}x^j y^{n - j} }
    Let x=1~\&~y=-1 look at the odd and the even terms.
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