A note on the Lalescu sequence
Year: 2025
Type: article
Abstract: The sequence$ a_n = \sqrt[n+1]{(n+1)!\, }-\sqrt[n]{n!\, } $is called the Lalescu sequence, after the Romanian mathematician Traian Lalescu (1882–1929). We prove that this sequence is monotonically decreasing.
Source: AIMS Mathematics
DOI: 10.3934/math.2025346
Authors: Carlo Mantegazza, Nicola Pio Melillo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,200
Funder: Università di Pisa
OpenAlex ID: W4409030867