If are positive real numbers then prove that
The Inequality is obvious for . So, let’s consider the case where . We will now divide the Inequality into two cases.
- Case 1st: Then it holds that
therefore, according to Bernulli’s Inequality it will hold that
- Case 2nd: Then it is
therefore, once again from Bernulli’s Inequality we get
and the proof is completed Q.E.D.