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Help: sum of binomial coefficents

  1. Oct 11, 2007 #1
    Help: sum of binomial coefficents !!

    I cannot figure out how to derive a closed formula for the sum of "the first s" binomial coefficients:

    [tex]\sum_{k=0}^{s} \left({{n}\atop{k}}\right)[/tex]

    with [tex]s<n[/tex]

    Could you please help me find out some trick to derive the formula... I've an exam on monday!!

    Thank you very much!!!
  2. jcsd
  3. Oct 11, 2007 #2
    Oh nevermind, I misread it as the sum of n binomial coefficients.
    Last edited by a moderator: Oct 11, 2007
  4. Jun 1, 2009 #3
    Re: Help: sum of binomial coefficents !!

    Dear Thealchemist83,

    I have just read your question, long after your exam... If this was your task, I wonder about the mark you've got because this sum does not have a closed form.:smile:

    See the fifth chapter of Concrete Mathematics (Graham, Knuth, Patashnik)

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