Re: The next exercise

[tomas]

On Fri, Dec 09, 2022 at 09:38:25PM +0100, Michael Heerdegen wrote:
> <tomas@tuxteam.de> writes:
> 
> > My choice was school maths [...]

[...]

> Or you remember how e can be introduced: with
> 
>          /    1\ n               /   1\ n+1
>   a_n := |1 + -|   and   b_n := |1 + -|  
>          \    n/                 \   n/  

FWIW, I started with the binomial formula,

  (1000 + 1)^1000 = 1000^1000 + (n-over-1) * 1000^999 + ...

Now n-over-1 is 1000, so we already have a 2 at the left
(more to come, of course :) Next (n-over-2) is 1000*999/1*2
(so roughly 1000*1000/2, that adds 0.5 to the most significant,
that makes 25...; Next 1000^3/6, so we are at 2666...

The denominator grows quickly (a tad more than an exponential),
so things are bound to converge quickly; besides, I over-estimated
things by setting 99x to 1000.

That already started looking a lot like e. Then I remembered
that limit I quoted from you above.

Then I asked Guile and Emacs.

Cheers
-- 
t

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