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Summation Proof with Binomial Theorem

  1. May 21, 2007 #1
    Prove the following statement:

    \sum\limits_{r + s = t} {\left( { - 1} \right)^r \left( \begin{array}{c}
    n + r - 1 \\
    r \\
    \end{array} \right)} \left( \begin{array}{c}
    m \\
    s \\
    \end{array} \right) = \left( \begin{array}{c}
    m - n \\
    t \\
    \end{array} \right)

    Any initial help is appreciated.
  2. jcsd
  3. May 26, 2007 #2


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    Staff Emeritus
    Science Advisor

    Well, what have you done? What is the definition of, say, m choose s?
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