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 Post subject: Geometric Mean
PostPosted: Tue Aug 09, 2016 8:06 pm 
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Find the geometric mean , with respect to the usual measure on the interval, of all the real numbers in the range $(0, 1]$.

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 Post subject: Re: Geometric Mean
PostPosted: Sat Oct 22, 2016 9:50 am 

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Nice one. The geometric mean with respect to the usual measure on the interval is actually defined as:

$$\mathcal{GM} = e^{\displaystyle \int_{0}^{1} \ln x \, dx} = e^{-1} = \frac{1}{e}$$

and this is our answer.

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