MathDB

inequality

Source:

November 24, 2010

inequalities

Problem Statement

x_1 + x_2 + \cdots + x_n = \sum_{i=1}^{n} x_i = \frac{1}{2}

and

x_i > 0

; then prove that:

\frac{1-x_1}{1+x_1} \cdot \frac{1-x_2}{1+x_2} \cdots \frac{1-x_n}{1+x_n} = \prod_{i=1}^{n} \frac{1-x_i}{1+x_i} \geq \frac{1}{3}