ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 64,   2   (1995)
pp.   283-285

NOTE ON AN INEQUALITY INVOLVING $(n!)^1/n$
H. ALZER


Abstract.  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.

AMS subject classification.  33B15, 26D99
Keywords

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