Geometric Mean
- Tolaso J Kos
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Geometric Mean
Find the geometric mean , with respect to the usual measure on the interval, of all the real numbers in the range $(0, 1]$.
Imagination is much more important than knowledge.
Re: Geometric Mean
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.
$$\mathcal{GM} = e^{\displaystyle \int_{0}^{1} \ln x \, dx} = e^{-1} = \frac{1}{e}$$
and this is our answer.
$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$
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