A Riemann-Type Theorem for Segmentally Alternating Series

Authors

Michał Banakiewicz, West Pomeranian University of Technology
Bruce Hanson, St. Olaf College
Pamela B. Pierce, The College of WoosterFollow
Franciszek Prus-Wiśniowski, Uniwersytet Szczeciński

Publication Date

10-2018

Document Type

Article

Volume

44

Issue

5

Abstract

We show that given any divergent series ∑���� with positive terms converging to 0 and any interval [��,��]⊂ℝ⎯⎯⎯⎯⎯ , there are continuum many segmentally alternating sign distributions (����) such that the set of accumulation points of the sequence of the partial sums of the series ∑�������� is exactly the interval [��,��] . We add some remarks on various segmentations of series with mixed sign terms in order to strengthen a sufficient criterion for convergence of such series.

Keywords

series segmentation, sign distribution, riemann rearrangement theorem

Recommended Citation

Banakiewicz, Michał; Hanson, Bruce; Pierce, Pamela B.; and Prus-Wiśniowski, Franciszek, "A Riemann-Type Theorem for Segmentally Alternating Series" (2018). Bulletin of the Iranian Mathematical Society, 44(5), 1303-1314. 10.1007/s41980-018-0092-z. Retrieved from https://openworks.wooster.edu/facpub/236