Bernoulli Inequality AM-GM proof

This is a proof of Bernoulli Inequality using Arithmetic Geometric Mean for the rational power, where the power is between 0 and 1. Note the inequality is reversed

Bernoulli Inequality by Mathematical Induction

Proving Bernoulli Inequality for Natural numbers using Mathematical Induction is easy and here is the proof. For rational Number we can use the AM-GM Inequality