Originally Posted by
Soroban 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 $\displaystyle j = 1, 2$ and add them up.
. . $\displaystyle \sum^2_{j=1}(i-j) \;=\;(i-1) + (i-2) \;=\;2i - 3$
Now that goes in the outer summation: .$\displaystyle \sum^3_{i=1}(2i - 3)$
Let $\displaystyle i = 1,2,3$ and add them up.
.$\displaystyle \sum^3_{i=1}(2i-3) \;=\;\bigg[2(1)-3\bigg] + \bigg[2(2)-3\bigg] + \bigg[2(3)-3\bigg] \;=\;-1 + 1 + 3 \;=\;3$