Title

A Riemann-Type Theorem for Segmentally Alternating Series

Document Type

Article

Publication Date

10-2018

Abstract

We show that given any divergent series ∑𝑎𝑛 with positive terms converging to 0 and any interval [𝛼,𝛽]⊂ℝ⎯⎯⎯⎯⎯ , there are continuum many segmentally alternating sign distributions (𝜖𝑛) such that the set of accumulation points of the sequence of the partial sums of the series ∑𝜖𝑛𝑎𝑛 is exactly the interval [𝛼,𝛽] . 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.

Department

Mathematics

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