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.
Citation: Carlo Mantegazza, Nicola Pio Melillo. A note on the Lalescu sequence[J]. AIMS Mathematics, 2025, 10(3): 7526-7539. doi: 10.3934/math.2025346
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.
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Carlo Mantegazza, Nicola Pio Melillo. A note on the Lalescu sequence[J]. AIMS Mathematics, 2025, 10(3): 7526-7539. doi: 10.3934/math.2025346
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