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Plz help with this combinatorial identity

  1. Sep 20, 2008 #1
    1. The problem statement, all variables and given/known data
    For positive integers n, r show that C(n+r+1, r) = C(n+r, r) + C(n+r-1, r-1) + ... + C(n+2, 2) + C(n+1, 1) + C(n, 0) = C(n+r, n) + C(n+r-1, n) + ... + C(n+2, n) + C(n+1, n) + C(n, n)

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Sep 20, 2008 #2


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    Staff Emeritus
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    You need to show some work before we can help with your homework. As a start, you could try stating the definitions of e.g. C(n+r+1, r).
  4. Sep 20, 2008 #3
    Sorry. I know the definition of C(n, r) = n!/[r!(n-r)!] but I still can't figure out the pattern. Are things supposed to cancel out?...other identities that I'm forgetting and could help in this question?
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