Note on special arithmetic and geometric means
Alzer, Horst
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994), p. 409-412 / Harvested from Czech Digital Mathematics Library
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We prove: If $A(n)$ and $G(n)$ denote the arithmetic and geometric means of the first $n$ positive integers, then the sequence $n\mapsto nA(n)/G(n)-(n-1)A(n-1)/G(n-1)$ $(n\geq 2)$ is strictly increasing and converges to $e/2$, as $n$ tends to $\infty $.

Publié le : 1994-01-01
Classification:  26A99,  26D15,  26D99,  40A05 
@article{118680,
     author = {Horst Alzer},
     title = {Note on special arithmetic and geometric means},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {35},
     year = {1994},
     pages = {409-412},
     zbl = {0806.26015},
     mrnumber = {1286588},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118680}
}

Alzer, Horst. Note on special arithmetic and geometric means. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) pp. 409-412. http://gdmltest.u-ga.fr/item/118680/

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