Geodesic
NOTE ON AN INEQUALITY INVOLVING $(n!)^1/n$
Acta mathematica Universitatis Comenianae, Tome 64 (1995) no. 2 
H. Alzer. NOTE ON AN INEQUALITY INVOLVING $(n!)^1/n$. Acta mathematica Universitatis Comenianae, Tome 64 (1995) no. 2. http://geodesic.mathdoc.fr/item/AMUC_1995_64_2_a9/
@article{AMUC_1995_64_2_a9,
     author = {H. Alzer},
     title = {NOTE {ON} {AN} {INEQUALITY} {INVOLVING} $(n!)^1/n$},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {1995},
     volume = {64},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_1995_64_2_a9/}
}
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Voir la notice de l'article provenant de la source Comenius University

We prove: If $G(n)=(n!)^1/n$ denotes the geometric mean of the first $n$ positive integers, then \frac1e^2<(G(n))^2-G(n-1)G(n+1) holds for all $n\geq 2$. The lower bound $\frac1e^2$ is best possible.