Yeah, that was the irony. I read a paper about reading math carefully, I ignored the intent of the paper entirely and skipped straight to the example, I saw 1+2+3+4+5=3x5, and I told my buddy, "Look, it's the product of the final number and the one that is two before it! So for 435, it's 435 times 433! Isn't that cool?"
And it's the final number +1 times the lower of the middle two if it's an even length sequence! So with modulo mapping between even and odd, we can easily construct a \sum that works for any n.