A Simple Generalization of the Arithmetic Mean – Geometric Mean Inequality

MCS Seminar by Prof. Ron Rietz
Wed., Dec. 9, 2009, 11:30 AM, Olin 321
The AM – GM inequality states that for positive numbers a_k, (1/n)(a₁ + a₂ + . . . + a_n) is greater than or equal to (a₁a₂…a_n)^1/n, with equality when and only when all of the terms a_k are equal. If some of the a_k are known values, not necessarily all equal, and the rest are allowed to vary, we will look at how close (in terms of difference, and in terms of ratio) the two means can be, and determine exactly when these extreme states occur. Only methods of basic calculus will be needed.

Refreshments will be served.