*Problem:*

If are positive real numbers then prove that

*Solution:*

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.*

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