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dan73
Posts:
467
From:
ct
Registered:
6/14/08


Re: The Many Roles of e
Posted:
Apr 21, 2013 6:36 AM


>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



