Title

A Riemann-Type Theorem for Segmentally Alternating Series

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

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