(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the summation notation satisfies the following property:

[itex]\displaystyle\sum\limits_{i=1}^n(\displaystyle\sum\limits_{j=1}^m aij) = \displaystyle\sum\limits_{j=1}^m(\displaystyle\sum\limits_{i=1}^n aij) [/itex]

2. Relevant equations

N/A

3. The attempt at a solution

[itex]\displaystyle\sum\limits_{i=1}^n(\displaystyle\sum\limits_{j=1}^m aij) = \displaystyle\sum\limits_{i=1}^n ai_{1} + \displaystyle\sum\limits_{i=1}^n ai_{2} + ... +\displaystyle\sum\limits_{i=1}^n ai_{n} = \displaystyle\sum\limits_{j=1}^m(\displaystyle\sum\limits_{i=1}^n aij) [/itex]

Have I proven this sufficiently or have I skipped a step? If I skipped a step, which one was it? Thanks in advance.

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# Homework Help: Summation proof.

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