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Combinatorial Identity

  1. Jun 22, 2005 #1
    Can someone help me how to deal with this identity that i must prove?

    [tex]{n + k-1 \choose n - 1} = \sum_{i=1}^k {k-1\choose i -1} {n \choose i}[/tex]

    I've tried to figure out what the combinatorial meaning of the right hand side is, but I didn't succeed :(
     
  2. jcsd
  3. Jun 22, 2005 #2
    I think it will help to rewrite it in the form:

    [tex]{n + k-1 \choose k} = \sum_{i=1}^k {k-1\choose k - i} {n \choose i}[/tex]
     
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