On Regrouping Convergent Series into Absolutely Convergent Series
Emilia Alvarez
Concordia University
Robert Raphael
Concordia University
Abstract
We demonstrate how any conditionally convergent series of real numbers can be regrouped as an absolutely convergent series. The regrouping can be expressed using a monotone subsequence of partial sums. The result can be extended to series of real-valued functions under specific conditions; these cases, as well as a constructive counterexample, are presented in detail.
