Criterion for irrational sequences
type: Item
instance of: scholarly article
title: Criterion for irrational sequences
zbMATH Open document ID: 0768.11021
author: Jaroslav Hančl
published in: Journal of Number Theory
publication date: 1993-05-16T00:00:00Z
review text: The main result of the paper is the following. Let \((a_ n)\) and \((b_ n)\) be two sequences of positive integers such that \(a_ n \geq r^{2^ n}_ n\) and \(b_{n+1} \leq r^ B_ n\) hold for all sufficiently large \(n\). Here \((r_ n)\) is a nondecreasing sequence of positive reals tending to infinity and \(B\) is a positive integer. Then the sum of the series \(\sum_{n \geq 1}b_ n/a_ n\) is an irrational number.
Mathematics Subject Classification ID: 11J72
zbMATH DE Number: 166061
zbMATH Keywords: irrational numbers
zbMATH Keywords: series of rational numbers
zbMATH Keywords: irratinal sequences
reviewed by: Cătălin Badea
MaRDI profile type: Publication
full work available at URL: jnth.1993.1010
OpenAlex ID: W1972487357
DOI: 10.1006/JNTH.1993.1010
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description: scientific article; zbMATH DE number 166061