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Math Help - Partial sum of 1-x

  1. #1
    iva
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    Partial sum of 1-x

    On WolframAlpha I see that the sum of x+1 is given by

    \displaystyle\sum_{i=0}^{n} -\frac{1}{2}(n-2)(n+1)

    But if I want to start at i=1 this sum is no longer valid!! Was a surprise at first but i see now it makes sense, but then what is the way to adjust these partial sum formulas for starting at different numbers, or do I have to think of a totally new formula when i want to do something like this?

    Thank you
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by iva View Post
    On WolframAlpha I see that the sum of x+1 is given by

    \displaystyle\sum_{i=0}^{n} -\frac{1}{2}(n-2)(n+1)

    But if I want to start at i=1 this sum is no longer valid!! Was a surprise at first but i see now it makes sense, but then what is the way to adjust these partial sum formulas for starting at different numbers, or do I have to think of a totally new formula when i want to do something like this?

    Thank you
    First something is weird with your indexes. You are summing over i but there are know i's in your formula!

    I assume you mean something like this

    Expand the sum out to get

    \displaystyle -\frac{1}{2}\left( \sum_{k=0}^{n}k^2- \sum_{k=0}^{n}k-\sum_{k=0}^{n}2\right)

    The sum or squares and the sum or the first n integers are known formula's
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