Author 
Topic: Floor Summation (Read 8581 times) 

ThudnBlunder
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489


Floor Summation
« on: Nov 9^{th}, 2009, 6:00am » 
Quote Modify

Evaluate 81ntanh/10^{n} ^{n=1}


IP Logged 
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.



Obob
Senior Riddler
Gender:
Posts: 489


Re: Floor Summation
« Reply #1 on: Nov 9^{th}, 2009, 2:18pm » 
Quote Modify

It's roughly 1  2.413 * 10^{264}. Are you looking for an actual precise answer, or is the point just that tanh pi is close to 1?

« Last Edit: Nov 9^{th}, 2009, 2:50pm by Obob » 
IP Logged 



ThudnBlunder
Uberpuzzler
The dewdrop slides into the shining Sea
Gender:
Posts: 4489


Re: Floor Summation
« Reply #2 on: Nov 11^{th}, 2009, 3:25am » 
Quote Modify

on Nov 9^{th}, 2009, 2:18pm, Obob wrote:It's roughly 1  2.413 * 10^{264}. Are you looking for an actual precise answer, or is the point just that tanh pi is close to 1? 
 As I am not expecting an exact answer, perhaps I should have put this elsewhere. The point is that the answer, a transcendental number, requires at least 239 decimal places before we can discover it does not equal 1. And even more if we want to consider rounding errors. Do you normally sum series to such precision?


IP Logged 
THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you.



Obob
Senior Riddler
Gender:
Posts: 489


Re: Floor Summation
« Reply #3 on: Nov 11^{th}, 2009, 6:10am » 
Quote Modify

I just observed that the first time floor(n tanh pi) != n1 occurs around n = 267 or so, summed the series 81(n1)/10^n = 1, and then gave as a rough error estimate an approximation of the difference between the two series. I guess I'm just saying that there is no reason to use tanh pi except for obfuscation; the real result lurking here is that lim_{x>1} sum (floor(n x))/10^n = 1, and that the convergence occurs very quickly.


IP Logged 



