Results 1 to 3 of 3

Thread: An Equality of Binomial Sums

  1. #1
    Newbie
    Joined
    Aug 2010
    Posts
    3

    An Equality of Binomial Sums

    If n\ge 0, show that

    \displaystyle \sum_{k=0}^{n}\binom{2n}{k}\binom{2n-2k}{n-k} = \sum_{k=0}^{n}\binom{2n+1}{k} = \sum_{k=0}^{2n}\binom{2n}{k}
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Mar 2008
    Posts
    934
    Thanks
    33
    Awards
    1
    Quote Originally Posted by Vandermonde View Post
    If n\ge 0, show that

    \displaystyle \sum_{k=0}^{n}\binom{2n}{k}\binom{2n-2k}{n-k} = \sum_{k=0}^{n}\binom{2n+1}{k} = \sum_{k=0}^{2n}\binom{2n}{k}
    This is false for n=2.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2010
    From
    Vancouver
    Posts
    432
    Thanks
    17
    The first one seems to the the odd one out. The last two evaluate to the same closed form expression. I suppose there is a typo in the first sum.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 4
    Last Post: Dec 17th 2011, 11:48 AM
  2. Proof of binomial sums
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Nov 8th 2011, 07:01 AM
  3. Replies: 3
    Last Post: Jul 15th 2010, 05:33 AM
  4. squaring sums, expand the given binomial sum.
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Apr 9th 2010, 11:50 PM
  5. Sums of Binomial Coefficients - proof by induction
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Jan 22nd 2010, 07:44 AM

Search Tags


/mathhelpforum @mathhelpforum