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Research Article | Open Access

A note on the Lalescu sequence

Carlo Mantegazza( ), Nicola Pio Melillo
Dipartimento di Matematica e Applicazioni "Renato Caccioppoli", Università di Napoli Federico Ⅱ & Scuola Superiore Meridionale, Napoli, Italy
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Abstract

The sequence

a n = ( n + 1 ) ! n + 1 − n ! n

is called the Lalescu sequence, after the Romanian mathematician Traian Lalescu (1882–1929). We prove that this sequence is monotonically decreasing.

Keywords

Lalescu sequenceStirling's formulaconvergencemonotonicity
CLC number: 40A05

References

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AIMS Mathematics
Volume 10 Issue 3,
March 2025
Pages 7526-7539
DOI: 10.3934/math.2025346

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Mantegazza C, Melillo NP. A note on the Lalescu sequence. AIMS Mathematics, 2025, 10(3): 7526-7539. https://doi.org/10.3934/math.2025346

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Received: 14 November 2024
Revised: 14 March 2025
Accepted: 19 March 2025
Published: 15 March 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)