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Mathemathicians define there is a limit, which a series(representing a number, as a process) converges to,
They make the philosophical leap of equating the 'limit' with a concrete number that has not been computed or fully represented(due being infinite). This error largely stems from the infinite series formula discarding the 'limit to 0' part of finite series formula;
This is only series formula that is indisputable(infinite formula is a castrated version of it):
Note "the proof" relies on this( 1−rn+1 and rn+1 → 0 for | r | < 1. ):
https://en.wikipedia.org/wiki/Geometric_series#Proof_of_convergence