Series that Converge Absolutely but Don't Converge
Robert Kantrowitz, Michael Schramm · College Mathematics Journal · 2012
SummaryIf a series of real numbers converges absolutely, then it converges. The usual proof requires completeness in the form of the Cauchy criterion. Failing completeness, the result is false. We provide examples of rational series that illustrate this point. The Cantor set appears in connection with one of the examples.