The Arithmetic-Logarithmic-Geometric Mean Inequality
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The arithmetic-logarithmic-geometric mean inequality states that if then .[more]
The area under on the interval is .
The area under the tangent at is .
The area under on the interval is , as in the left graphic.
The area of the left trapezoid is .
The area of the right trapezoid is .
Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa (March 2011)
Open content licensed under CC BY-NC-SA
Reference: R. B. Nelsen, "Proof without Words: The Arithmetic-Logarithmic-Geometric Mean Inequality," Mathematics Magazine 68(4), 1995 p. 305.