A note on the Lalescu sequence
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.
Authors
- Carlo Mantegazza
- Nicola Pio Melillo
Publication Details
- Journal
- AIMS Mathematics
- Published
- 2025-01-01
- DOI
- https://doi.org/10.3934/math.2025346
- Primary Topic
- Mathematical Approximation and Integration
- Type
- article
- Field-Weighted Citation Impact
- 0.00