>>13038209you can't do this bro, the series doesn't converge so S does not make sense in the first place
now, if you took something like 1-1/2+1/3-1/4 etc. and played around with it a bit, you'd notice that you again get weird self-contradictory shit, but there's a perfectly good reason for that: there's a theorem of Riemann's that states that a *conditionally* convergent series can be rearranged to converge to literally any value you'd like. this stands in contrast to absolutely convergent series, which remain the same under any rearrangement. that is, conditionally convergent series don't really have anything meaningful to say
