Arithmetic - geometric means inequality

Let \(x_1, x_2, \ldots , x_n\) be nonnegative real numbers. Then

\[\frac{1}{n}\sum_{i = 1}^{n}x_{i} \geq \left(\prod_{i = 1}^{n}x_{i}\right)^{1/n},\]

and equality holds if and only if \(x_1 = x_2 = \cdots = x_n\).