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Homework Help: Find an expression for the sum of the series

  1. Feb 29, 2012 #1
    1. The problem statement, all variables and given/known data

    (1x2x6) + (2x3x7) + ... + n(n + 1)(n + 5)



    2. Relevant equations

    Find an expression for the sum of the series. Give your answer as a product of linear factors in n.


    3. The attempt at a solution

    I haven't tried it since I don't know what to do.
     
  2. jcsd
  3. Feb 29, 2012 #2

    Delphi51

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    Homework Helper

    I haven't seen one of those for years! They are interesting. There is some theory saying that the sum is equal to a polynomial with one degree higher than the term. Your terms are 3rd degree, so you need a 4th degree polynomial:
    S = a*n^4 + b*n^3 + c*n^2 + d*n + e
    By hand you figure out the sum and the powers for n = 1, 2, 3, 4, and 5.
    That gives you a system of 5 equations with 5 unknowns a, b, c, d, e.
    Solve the system to get the unknown coefficients.
     
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