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Means to an End

by Richard P. Kubelka

This article originally appeared in:
Mathematics Magazine
April, 2001

Subject classification(s): Calculus | Single Variable Calculus | Limits
Applicable Course(s): 3.2 Mainstream Calculus II | 3.5 Non-mainstream Calc II

The 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
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