by Richard P. Kubelka
This article originally appeared in:
Mathematics Magazine
April, 2001
Subject classification(s):
Calculus | Single Variable Calculus | LimitsApplicable Course(s):
3.2 Mainstream Calculus II | 3.5 Non-mainstream Calc IIThe limit of the geometric mean of the first \(n\) integers raised to the real positive power \(s\), divided by their arithmetic mean is shown to be \((s+1)/e^s\). An elementary derivation of Stirling`s approximation suggested this limit for \(s=1\).
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Capsule Course Topic(s):
One-Variable Calculus | Infinite Limits: Function Values and Integrals