tl;dr: there is no "real" or "one" kind of maths, you'll have to first pick which field of mathematics you're working with. Arithmetics? Then no: 1+2+3+... is a

tl;dr: there is no "real" or "one" kind of maths, you'll have to first pick which field of mathematics you're working with. Arithmetics? Then no: 1+2+3+... is a divergent sum. Using calculus, specifically analytic continuation on the an Euler series? Then yeah, you can apply the rules in such a way that you get this answer and it's a mighty useful identity that can be exploited in complicated proofs.