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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


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    I don't believe there is any such formula.
  4. Oct 14, 2007 #3
    well, i think there is one, because as long as i remember i have seen it in a textbook, but it is quite long i think, and i cannot remember how it was right now. I am gonna look at it.
  5. Oct 14, 2007 #4
    Last edited: Oct 14, 2007
  6. Oct 15, 2007 #5


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    Your answer 2n is for s=n, the original question was for s<n.
  7. Oct 15, 2007 #6
    No formula exists in this case. See the book A=B for how to simplify binomial summations. There exists simple algorithms that will yield a formula or will tell you that no formula exists.
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