Is the inequality true for all $n\geq 2$?

It's wrong for any $n\geq5$.

For $n=5$ try $x=1.1$ and $y=z=1$.

For $n=4$ and $n=3$ it's true.

Tags:

Inequality

Summation

Factoring

A.M. G.M. Inequality

Sum Of Squares Method

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