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The Arithmetic-Logarithmic-Geometric Mean Inequality


	The arithmetic-logarithmic-geometric mean inequality states that if then . Left graphic: The area under on the interval is . The area under the tangent at is . Then . Right graphic: 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 . Then .


	Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa
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Reference: R. B. Nelsen, "Proof without Words: The Arithmetic-Logarithmic-Geometric Mean Inequality," Mathematics Magazine 68(4), 1995 p. 305.

"The Arithmetic-Logarithmic-Geometric Mean Inequality" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/TheArithmeticLogarithmicGeometricMeanInequality/

Contributed by: Soledad Mª Sáez Martínez and Félix Martínez de la Rosa

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