Note on the irrationality of certain infinite series

Pavel Rucki
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 1, Pages 5–14
DOI: 10.7546/nntdm.2026.32.1.5-14
Full paper (PDF, 213 Kb)

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Authors and affiliations

Pavel Rucki
Department of Mathematical Methods in Economics, Faculty of Economics, VŠB – Technical University Ostrava
17. listopadu 2172/15, 708 00 Ostrava-Poruba, Czech Republic

Abstract

The aim of this paper is to introduce new criteria for real infinite series that satisfy a specific property and yield an irrational sum. These criteria are based on an extension of previous ideas proposed by Erdős. The paper includes several illustrative examples.

Keywords

• Irrationality, Transcendence
• Liouville number
• Infinite series

2020 Mathematics Subject Classification

• 11J72
• 11J82

References

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Manuscript history

• Received: 1 October 2025
• Revised: 15 December 2026
• Accepted: 6 February 2026
• Online First: 12 February 2026

Copyright information

Ⓒ 2026 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).