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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


    Staff: Mentor

    why dont you compute the first 5 terms of the series and see if you notice a pattern

    n=1 sum=12
    n=2 sum=54
    n=3 ...

    then divide each sum by n and see if you can find a pattern in terms of n
  4. Feb 29, 2012 #3
    Ok, so I have:

    12/n + 42/n + 96/n + 180/n + 300/n

    All I can see is that each number has a highest common denominator of 6, but I'm guessing that's not it.
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