*Problem:*

Let be positive real numbers. Prove that

*Solution:*

It holds for every positive number that

.

Back to our inequality now, rewrite it as follows:

.

Using the above result we have that

.

Let us now make the final step for the proof of our inequality. From Bernulli’s inequality we get that

,* Q.E.D.*

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*Related*

Dear George,

in problem 32, are you sure that

Isn’t the quantity negative by taking, for instance, ?

Well, you are right. I just forgot to mention that and imply that