If for , prove that

*Proof.*For not all equal, we may apply the previous exercise with and with , to obtain,

Further, if , then

Thus, the requested inequality holds for any , and as a bonus, we prove equality holds if and only if

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Stumbling Robot

A Fraction of a Dot
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Use the pth power mean to prove an inequality

* Proof. * For not all equal, we may apply the previous exercise with and with , to obtain,

If for , prove that

Further, if , then

Thus, the requested inequality holds for any , and as a bonus, we prove equality holds if and only if