I got this "proof" that showed 1+2+3+4+...=-1/12 from a knowledgeable friend about one and a half months ago now. On first glance, I dismissed his proof as probably wrong as the proof seemed counterintuitive and not in line with how we would expect a diverging series to behave. Here goes.

I have asked around from my seniors(I am in Year 1 of a "high school" that starts at 13 and continues for 6 straight years until 18) but I still am not sure what is wrong with the proof apart from some possible notation errors. What is wrong with his "proof" or is he actually correct? s and all its other subscript variants are variables. The first mention of one such variable defines it.