Welcome to mathimatikoi.org forum; Enjoy your visit here.

## Geometric Mean

General Mathematics
Tolaso J Kos
Articles: 2
Posts: 854
Joined: Sat Nov 07, 2015 6:12 pm
Location: Larisa
Contact:

### 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.
Riemann
Articles: 0
Posts: 169
Joined: Sat Nov 14, 2015 6:32 am
Location: Melbourne, Australia

### Re: Geometric Mean

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

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

$\displaystyle \sum_{n=1}^{\infty}\frac{1}{n^s}= \prod_{p \; \text{prime}}\frac{1}{1-p^{-s}}$