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Exploring Pentation - Base e
#23
I took

I added asymtotic values of negative infinite of base e heptation and [9] to the sum I mentioned before:

Sum [5] =1/1,85035452902718^8-1/(2*1,8503545290271Cool^7+1/(3*1,8503545290271Cool^6-1/(4*1,8503545290271Cool^5+1/(5*1,8503545290271Cool^4=0,007297583=1/137,0316766

From Andrew's graph, I found the values to be roughly e[7]-infinity = -3,751 and e[9]-infinity = -5,693.

Then I put them in the same sum, obtaining:

Sum [7] =1/3,751^8-1/(2*3,751)^7+1/(3*3,751)^6-1/(4*3,751)^5+1/(5*3,751)^4=3,20285E-05

Sum[9] = 1/5,693^8-1/(2*5,693)^7+1/(3*5,693)^6-1/(4*5,693)^5+1/(5*5,693)^4=3,15992E-05

Then I made Sum [5,7,9] = Sum[5]-Sum[7]+Sum[9] = 0,007297583-3,20285E-05+3,15992E-05=0,0072971534=1/137,039738252

So after this, approximation of alpha =0.07297352570(5) got even better, as I expected, but of course I do not know the exact values of e[7]-infinity and e[9]-infinity and more.

Then we could see how does the sum Sum[5]-Sum[7]+Sum[9]-Sum[11]+Sum[13]-Sum[15]+.........converge.

Ivars
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Messages In This Thread
Exploring Pentation - Base e - by jaydfox - 12/18/2007, 02:57 PM
RE: Exploring Pentation - Base e - by andydude - 12/18/2007, 04:45 PM
RE: Exploring Pentation - Base e - by jaydfox - 12/19/2007, 06:01 AM
RE: Exploring Pentation - Base e - by Ivars - 01/28/2008, 11:01 AM
RE: Exploring Pentation - Base e - by Ivars - 02/02/2008, 05:05 PM
RE: Exploring Pentation - Base e - by Ivars - 02/02/2008, 10:50 PM
RE: Exploring Pentation - Base e - by GFR - 02/02/2008, 11:01 PM
RE: Exploring Pentation - Base e - by Ivars - 02/04/2008, 08:07 PM
RE: Exploring Pentation - Base e - by quickfur - 02/22/2008, 12:21 AM
RE: Exploring Pentation - Base e - by GFR - 02/04/2008, 09:19 PM
RE: Exploring Pentation - Base e - by Ivars - 02/05/2008, 11:25 PM
RE: Exploring Pentation - Base e - by GFR - 02/06/2008, 03:01 PM
RE: Exploring Pentation - Base e - by Ivars - 02/06/2008, 06:23 PM
RE: Exploring Pentation - Base e - by Ivars - 02/07/2008, 09:00 PM
RE: Exploring Pentation - Base e - by Ivars - 02/07/2008, 09:30 PM
RE: Exploring Pentation - Base e - by Ivars - 02/07/2008, 11:20 PM
RE: Exploring Pentation - Base e - by Ivars - 02/08/2008, 10:32 AM
RE: Exploring Pentation - Base e - by Ivars - 02/08/2008, 10:51 AM
RE: Exploring Pentation - Base e - by Ivars - 02/08/2008, 10:56 AM
RE: Exploring Pentation - Base e - by Ivars - 02/09/2008, 11:12 PM
RE: Exploring Pentation - Base e - by Ivars - 02/15/2008, 08:24 PM
RE: Exploring Pentation - Base e - by Ivars - 03/03/2008, 08:04 PM

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