[PD] exponential tempo control

[Chuckk Hubbard]

I should be writing math textbooks.
What does anyone use this particular equality for?


On 10/30/05, Mathieu Bouchard <matju at artengine.ca> wrote:
>
> 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.
>
> ____________________________________________________________________
> Mathieu Bouchard - tél:+1.514.383.3801 - http://artengine.ca/matju
> Freelance Digital Arts Engineer, Montréal QC Canada
>



--
"It is not when truth is dirty, but when it is shallow, that the lover of
knowledge is reluctant to step into its waters."
-Friedrich Nietzsche, "Thus Spoke Zarathustra"
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