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Math Help - Help needed on sum of product combinations

  1. #1
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    Help needed on sum of product combinations

    Does anyone know how to calculate a sum of all i-element product combinations from a k-element set of ordered natural numbers say {n,n-1,..,n-k+1}. I mean how to express it in a hopefully short equation rather than doing it manually. If we denote this sum by S_i^k(n) then an example of such sum S_2^4(6)=
    3*4+3*5+3*6+4*5+4*6+5*6.

    which is a sum of all 2 element products from the 4-element set of natural numbers ending on 6: {3 4 5 6}.

    Help would be greatly appreciated and would help to solve distibution of a real problem in telecommunication industry

    Best
    Last edited by dymitrruta; March 4th 2009 at 05:45 AM. Reason: typo
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