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Math Help - Algebraic Manipulation

  1. #1
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    Algebraic Manipulation

    I have a math problem where the expression:

    \displaystyle\sum_{i=0}^{n-1}(i+1)(n-i)

    is changed to:

    \displaystyle\sum_{i=1}^{n}i(n+1-i)

    but I am having difficulty understanding how this is achieved.
    Can anyone explain how this is done?

    Thanks
    Last edited by wmassey; March 23rd 2010 at 02:55 PM.
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  2. #2
    Member pflo's Avatar
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    Quote Originally Posted by wmassey View Post
    I have a math problem where the expression:

    \displaystyle\sum_{i=0}^{n-1}(i+1)(n-i)

    is changed to:

    \displaystyle\sum_{i=1}^{n}i(n+1-i)

    but I am having difficulty understanding how this is achieved.
    Can anyone explain how this is done?

    Thanks
    In the second expression the i is one greater than it is in the first one because it starts at 1 (not 0) and goes to n (not n-1). You could account for this by subtracting one from the i when changing the limits of the summation:
    \displaystyle\sum_{i=0}^{n-1}[i+1][n-i]
    \displaystyle\sum_{i=1}^{n}[(i-1)+1][n-(i-1)]
    \displaystyle\sum_{i=1}^{n}i(n+1-i)

    Does that make any sense?
    Last edited by pflo; March 23rd 2010 at 03:19 PM.
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  3. #3
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    Yea I understand it now - thanks pflo!
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