## AG inequality

### Task number: 2799

Prove this inequality between the geometric and arithmetic means of a set of numbers.

For non-negative \(x_1,…,x_n\): \( \displaystyle \sqrt[n]{x_1x_2\cdots x_n} \le \frac{x_1+x_2+…+x_n}n \)

#### Variant 1

For \(n=2\).

#### Variant 2

When \(n\) is a power of two.

#### Variant 3

For any \(n\in \mathbb N\).