From the power mean inequality why does ?
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Originally Posted by particlejohn From the power mean inequality why does ? There's a proof in this link: Generalized mean - Wikipedia, the free encyclopedia
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.
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