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Math Help - Summation Notation question help

  1. #1
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    Question Summation Notation question help

    Hi

    I have this practice question but I have no idea how to approach.
    Any help guiding me on the theory of how to do this question is appreciated.

    Summation Notation question help-calc.jpg

    Thanks
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  2. #2
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    Re: Summation Notation question help

    Just in case a picture helps...




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  3. #3
    MHF Contributor Siron's Avatar
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    Re: Summation Notation question help

    For part (a):
    You're given:
    \overline{X}=n^{-1}\sum_{i=1}^{n}X_i (expression (1)) and you need to prove that: \sum_{i=1}^{n}(X_i-\overline{X})=0 (expression (2))
    Substitute (1) in (2):
    \sum_{i=1}^{n} \left(X_i-n^{-1}\sum_{i=1}^{n}X_i\right)
    To see clearly what happens we write down a few terms of the summation:
    [X_1-n^{-1}(X_1+X_2+\ldots+X_n)]+[X_2-n^{-1}(X_1+X_2+\ldots+X_n)]+\ldots+[X_n-n^{-1}(X_1+X_2+\ldots+X_n)]
    this is equal to:
    (X_1+X_2+\ldots+X_n)-nn^{-1}(X_1+X_2+\ldots+X_n)=0
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  4. #4
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    Re: Summation Notation question help

    Hi guys thanks for the help
    Thankyou
    Last edited by abc1993; March 9th 2012 at 12:48 AM.
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