# Means to an End

by Richard P. Kubelka

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 $$s=1$$.

A pdf copy of the article can be viewed by clicking below. Since the copy is a faithful reproduction of the actual journal pages, the article may not begin at the top of the first page.