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Summation combinatorics

  1. Mar 9, 2010 #1
    how do I evaluate [tex] \sum_{k=0}^d \binom{n+d-k}{n} [/tex] ?
     
  2. jcsd
  3. Mar 9, 2010 #2
    Re: summation/combinatorics

    I don't know the method. But first you could change the variable of integration to [itex]k'=d-k[/itex] and then you look it up :)
    I think the answer is
    [tex]\binom{n+d+1}{d}[/tex]
     
  4. Jun 15, 2010 #3
    Re: summation/combinatorics

    The answer is:
    [tex]\left(
    \begin{array}{c}
    n+d+1 \\
    n+1
    \end{array}
    \right)[/tex]

    Please refer to:

    http://www.voofie.com/content/76/evaluating-summation-involving-binomial-coefficients/" [Broken]

    for the steps and how to deal with problem of this type.
     
    Last edited by a moderator: May 4, 2017
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