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I have that question: $$ \sum_{i=1}^{n}\sum_{j=i+1}^{n} a_{i,j} $$ I try to understand how to sum this double summation works, so I try to sum it up to 3, but so far managed to find 3 different solutions. $$ 1.(a_{1,2}+a_{1,2}+a_{2,3}) $$$$ 2.(a_{1,2}+a_{1,3}+a_{2,1}+a_{2,3}) $$$$ 3.(a_{1,2}+a_{1,3}+a_{2,3}+a_{3,3}) $$

I think that the first could be the right one but im not sure. which one of them is right?

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$$\sum_{i=1}^{3}\sum_{j=i+1}^{3} a_{i,j} = \left( \sum_{j=2}^3 a_{1,j}\right) + \left( \sum_{j=3}^3 a_{2,j}\right) + \left( \sum_{j=4}^3 a_{3,j}\right) = a_{1,2} + a_{1,3} + a_{2,3} $$

so none of your options are correct.

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