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 \(n\in \mathbb N\).

Difficulty level: Hard task
Proving or derivation task
Cs translation
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