2021-01-06

## real analysis – Proofs of AM-GM inequality

The Question : 108 people think this question is useful The arithmetic – geometric mean inequality states that $$\frac{x_1+ \ldots + x_n}{n} \geq \sqrt[n]{x_1 \cdots x_n}$$ I’m looking for some original proofs of this inequality. I can find the usual proofs on the internet but I was wondering if someone knew a proof that is