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.

Published
2019-03-27
How to Cite
ALVAREZ, Emilia; RAPHAEL, Robert. On Regrouping Convergent Series into Absolutely Convergent Series. Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 4, n. 1, mar. 2019. ISSN 2378-5810. Available at: <https://mjum.math.umn.edu/index.php/mjum/article/view/66>. Date accessed: 20 oct. 2020.
Section
Articles