(Of course the negative number always has to be below the sigma!) Notice how the variables m & x swap places. The variable below the sigma has to be multiplied by -1. You know that gives you a number's additive inverse, don't you?
(-3) + (-2) + (-1) + 0 + 1 + 2 + 3 + 4 + 5 = 4 + 5 = 9
[All of the additive inverses cancel each other out & you're left with 4 & 5 adding up to 9! Just below is the negative version of this summation!]
(-5) + (-4) + (-3) + (-2) + (-1) + 0 + 1 + 2 + 3 = (-5) + (-4) = -9
Here's Miss Zero Digit representing the number zero again! You may have already seen her in "Super Summation 2". This math trick is a sequel to it; plus, it's very similar to it!
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© Derek Cumberbatch