(July 21, 2023 at 2:54 pm)Loaded dice Wrote:(March 8, 2023 at 4:47 pm)GrandizerII Wrote: Doing algebra with infinite series is tricky
It's wrong. All the basic rules you know about manipulating and rearranging the terms of a finite sum, are no longer true in general when it comes to infinite series.
The first thing to do with an infinite series is to study its convergence. If it is convergent, in some cases it's possible to rearrange its terms without losing convergence (e.g. https://en.wikipedia.org/wiki/Riemann_series_theorem)
It's useful to remember that the entire topic of infinite series is serious undergraduate math, if you're not familiar with basic real analysis and sequences just forget them for now.
Yeah, my analysis in the OP was wrong. Since the series is not convergent, the problem starts from the very beginning (as polymath stated).
