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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 .

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Reference: R. B. Nelsen, "Proof without Words: The Arithmetic-Logarithmic-Geometric Mean Inequality," Mathematics Magazine 68(4), 1995 p. 305.

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"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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