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Math Help - double summation

  1. #1
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    double summation

    Been trying to get this problem for a few hours. Been going through the book and online for some examples but haven't found anything that makes sense.

    If someone could help me that would be gooood.

    Compute the double sum:

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  2. #2
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    Hello, premierplayer!

    If you don't understand a basic summation,
    . . all the examples in the world won't help you.


    Compute the double sum: . \sum^3_{i=1} \sum^2_{j=1} (i-j)

    In the inner summation, let j = 1, 2 and add them up.

    . . \sum^2_{j=1}(i-j) \;=\;(i-1) + (i-2) \;=\;2i - 3

    Now that goes in the outer summation: . \sum^3_{i=1}(2i - 3)
    Let i = 1,2,3 and add them up.

    . \sum^3_{i=1}(2i-3) \;=\;\bigg[2(1)-3\bigg] + \bigg[2(2)-3\bigg] + \bigg[2(3)-3\bigg] \;=\;-1 + 1 + 3 \;=\;3

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, premierplayer!

    If you don't understand a basic summation,
    . . all the examples in the world won't help you.



    In the inner summation, let j = 1, 2 and add them up.

    . . \sum^2_{j=1}(i-j) \;=\;(i-1) + (i-2) \;=\;2i - 3

    Now that goes in the outer summation: . \sum^3_{i=1}(2i - 3)
    Let i = 1,2,3 and add them up.

    . \sum^3_{i=1}(2i-3) \;=\;\bigg[2(1)-3\bigg] + \bigg[2(2)-3\bigg] + \bigg[2(3)-3\bigg] \;=\;-1 + 1 + 3 \;=\;3

    Awesome.

    So I pressume that the number above the sumation has to do with how many times we calculate.

    for example 2 is (i-1) + (i-2)... etc..

    I get it. Thanks.
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