It is not well defined. Because an order of summation is not given you could just as easily sum pairs of (0,1), (-1,2), (-2,3), (-3,4)… (-x, x+1) and conclude you are constantly adding 1 to your total so it goes to infinity instead
Or do the reverse of (-1,0), (-2,1), … (-x-1, x) and get that the each pair adds -1 so the sum goes to negative Infinity
Order of the addition sometimes changes infinite sums. Infinitely large things are weird sometimes
It is not well defined. Because an order of summation is not given you could just as easily sum pairs of (0,1), (-1,2), (-2,3), (-3,4)… (-x, x+1) and conclude you are constantly adding 1 to your total so it goes to infinity instead
Or do the reverse of (-1,0), (-2,1), … (-x-1, x) and get that the each pair adds -1 so the sum goes to negative Infinity
Order of the addition sometimes changes infinite sums. Infinitely large things are weird sometimes