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Topic: The Many Roles of e
Replies: 8   Last Post: Apr 23, 2013 8:39 AM

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dan73

Posts: 458
From: ct
Registered: 6/14/08
Re: The Many Roles of e
Posted: Apr 21, 2013 6:36 AM
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>A slight twist to the above equation ties pi
>with (e) on a convergence too (4).


>Where n = pi or a multiple of pi.

>4~(in(( 2+2^n)/(2^n -2)^2^n))

>When n=pi =4.07067...
>"""""n=2pi =4.000879...
>"""""n=3pi =4.000011290...
>"""""n=4pi =4.000000144973...
>"""""n=5pi =4.000000001861...

...
>"""""n=10pi =4.00000000000000000064972...
...
>"""""n=100pi =4.000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000003839495388522987805741...

>It appears that each multiple of pi adds almost 2 zeros
>to the decimal expansion of (4)


This will converge on all even integers > 2 by
changing the formula for each even number convergence.

When (n) = pi or a multiple of pi.
4~(in(( 2+2^n)/(2^n -2)^2^n))
6~(in(( 3+3^n)/(3^n -3)^3^n))
8~(in(( 4+4^n)/(4^n -4)^4^n))
10~(in(( 5+5^n)/(5^n -5)^5^n))
12~(in(( 6+6^n)/(6^n -6)^6^n))
14~(in(( 7+7^n)/(7^n -7)^7^n))
etc.
A more rapid convergence happens as each even get
larger and with more pi multiples of (n).

Dan



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