Results 1 to 3 of 3

Math Help - Combinatorical Identity

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    16

    Combinatorical Identity

    I've been thinking on this problem for 2 days but I haven't found even a clue. The question is to prove the correctness of the following identity:
    \displaystyle \sum _{k=0}^{p} {p\choose k}^{2}{n+2\,p-k\choose 2\,p}= {n+p\choose p} ^{2}
    Could you give me a hint about how to prove this?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Nov 2009
    Posts
    130
    Using mathematical induction I guess would be the easier way.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    16
    Quote Originally Posted by p0oint View Post
    Using mathematical induction I guess would be the easier way.
    Yes I know, but I think it's hard to use induction because it has power. BTW, it has two variables. I don't know how to use induction when there are two variables.

    EDIT: I think it can be solved with double counting. But I don't what I should count in two different ways.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Combinatorical proof
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: July 13th 2010, 08:59 PM
  2. Identity
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: May 2nd 2010, 06:09 PM
  3. combinatorical proof
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: October 24th 2009, 05:01 PM
  4. identity
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: June 7th 2008, 12:26 PM
  5. Beautiful combinatorical problem
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: October 28th 2007, 09:51 AM

Search Tags


/mathhelpforum @mathhelpforum