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Proving this binomial identity

  1. Apr 17, 2009 #1
    [tex]\sum_{m=k}^{n-k}\binom{m}{k}\binom{n-m}{k}=\binom{n+1}{2k+1}[/tex]


    I'm not sure how to prove it, I understand the combinatorial proof..i.e. putting it to an example...but i can't derive one side and get the other.
     
  2. jcsd
  3. Apr 17, 2009 #2
    How do you understand the combinatorial proof but not know how to prove it?
     
  4. Apr 18, 2009 #3
    It was an example given in the book. I just don't see how they manipulated the binomial to move the stuff around.
     
  5. Apr 18, 2009 #4
    Suppose you had a bag full of n balls. Suppose out of the n balls you had m green ones. Would the right hand side be adding up the ways to count all the gree balls and non-green balls. I didn't even really understand this reasoning. This identity is really frustrating me.
     
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