From the power mean inequality why does ?

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- Aug 29th 2008, 09:37 PMparticlejohnPower mean
From the power mean inequality why does ?

- Aug 29th 2008, 10:12 PMmr fantastic
There's a proof in this link: Generalized mean - Wikipedia, the free encyclopedia

- Aug 30th 2008, 06:16 AMPaulRS
First:

Now we have: (since what's inside the logarithm tends to 1)

So: (by the linearity of the limit- all of those are defined-)

So: and the rest follows easily by the properties of the logarithm and the continuity of the exponential function.