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Math Help - double summations:

  1. #1
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    double summations:

    n m
    Σ Σ Xij
    i=1 j=1
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  2. #2
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    Re: double summations:

    Hello, nassaufashionista!

    What is the question?


    \displaystyle\sum^n_{i=1} \sum^m_{j=1}X_{ij}

    Are we expected to expand it?

    \displaystyle\sum^n_{i=1} \sum^m_{j=1}X_{ij} \;=\;\sum^n_{i=1}\big(X_{i1} + X_{i2} + X_{i3} + \cdots + X_{im}\big)

    . . . . . . . . =\;\begin{Bmatrix}\;\;\;(X_{11} + X_{12} + X_{13} + \cdots + X_{1m}) \\ + (X_{21} + X_{22} + X_{23} + \cdots + X_{2m}) \\ + (X_{31} + X_{32} + X_{33} + \cdots + X_{2m}) \\ \vdots \qquad \qquad \vdots \qquad \qquad \vdots \\ + (X_{n1} + X_{n2} + X_{n3} + \cdots + X_{nm}) \end{Bmatrix}
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  3. #3
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    Re: double summations:

    Ok Thank you! i was looking at another double summation:

    2 3
    Σ Σ Xij
    i=1 j=1

    The expansion in my text is as follows:
    (x11+x12+{x13}+x21+x22+x23
    ^i dont understand why the x13 is used because i is only 1 to 2...
    can you explain the x13 in parenthesis and explain the expansion I think i may have missed something.
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