[PD] exponential tempo control

[Mathieu Bouchard]

On Sat, 29 Oct 2005, Chuckk Hubbard wrote:

> Just a note, I came up with a pretty obvious proof for:
>  SUM (k=0 to N-1) i^k = (i^N - 1) / (i - 1)
>   (i - 1) (i^0 + i^1 + i^2 + .... + i^(N-1))
> =
> -i^0 + i^1 - i^1 + i^2 - i^2 ... + i^(N-1) - i^(N-1) + i^N
> = i^N - 1
> All the terms cancel except the lowest and highest powers of i.

That's the same proof that is used in all math textbooks.

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Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
Freelance Digital Arts Engineer, Montréal QC Canada