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*To*: seul-edu@seul.org*Subject*: Re: [seul-edu] [OT] summation of 1/2x*From*: Jan Hlavacek <jhlavacek@sf.edu>*Date*: Wed, 5 Apr 2000 13:06:15 -0500*Delivery-Date*: Wed, 05 Apr 2000 14:06:03 -0400*In-Reply-To*: <4.3.2.20000405161532.00a84100@pop.free.fr>; from giem@free.fr on Wed, Apr 05, 2000 at 04:25:00PM +0100*Mail-Followup-To*: seul-edu@seul.org*References*: <00040420542300.00442@CorelLinux> <00040420542300.00442@CorelLinux> <20000405094726.A13914@math.sf.edu> <4.3.2.20000405161532.00a84100@pop.free.fr>*Reply-To*: seul-edu@seul.org*Sender*: owner-seul-edu@seul.org

On Wed, Apr 05, 2000 at 04:25:00PM +0100, jm wrote: > > > > I got to thinking of this last week when a friend and I were trying to > > > remember what the summation of 1/x evaluated from x=0 to x=infinity > > > is. > > > >I would like to see what you found! ;-) > > If I remember well, there is a trick to calculate the sum of 1/2x from 1 to > infinity > you just need a sheet of paper: > + first you cut in half the sheet of paper: you get 1/2 sheet and another > 1/2 sheet > + then you cut in half again one of the 1/2 sheet: you get 1/4 and 1/4 > + then you cut in half again... > > so you can prove that 1/2+1/4+1/8+..+1/2n+.. = 1 Actually, that is 1/2^n (one over 2 to the n), not 1/2n. As a matter of fact, the series 1/n does not have a finite sum. But after adding some terms at the beginning, the sum increases so slowly that from a computer calculation, it may indeed seem like you have a convergence. After adding first 10000 terms, it all looks like 9.787..., and it seems that these digits are not changing any more. But after adding first 100000 terms you get 12.0901..., and so on. It keeps increasing, and it is not bounded. Of course, when you get so far that your computer thinks that 1/n = 0, you have the "limit" :-). Then you increase the precission, and your "limit" suddenly changes. This is a classical example that demonstrates shortcommings of numerical computations in math. Even better example is 1/(n*ln(n)) (ln stands for natural logarithm). This series is also divergent, but the sum increases even slower than the sum of 1/n. -- Jan Hlavacek (219) 434-7566 Department of Chemistry Jhlavacek@sf.edu University of Saint Francis http://199.8.81.3/Jhlavacek/

**References**:**[seul-edu] Long, long ago...***From:*bgfay <rid24199@ride.ri.net>

**Re: [seul-edu] Long, long ago...***From:*Jan Hlavacek <jhlavacek@sf.edu>

**[seul-edu] [OT] summation of 1/2x***From:*jm <giem@free.fr>

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