Re: Sum of infinite series

["Paul O. Johnson" <pojhome@SWBELL.NET>]

Laurent,

After failing to understand the earlier replies to my question, I can follow
yours easily. So my series diverges. How would I easily find the sum of the
first 50 or 100 terms such as John Denker suggests in his second reply?

Paul O. Johnson

----- Original Message -----
From: "Laurent Hodges" <lhodges@IASTATE.EDU>
To: <PHYS-L@lists.nau.edu>
Sent: Friday, January 25, 2002 10:51 AM
Subject: Sum of infinite series


> > I want to state in the exhibit's sign what the absolute maximum extension
> > is. This requires that I sum the infinite series 1/2 + 1/4 + 1/6 + 1/8 +
. . .
> > Paul O. Johnson
>
> This can be grouped, after the first two terms, into 2 terms each larger
> than or equal to 1/8 (thus summing to over 1/4), followed by 4 terms each
> larger than or equal to 1/16 (thus summing to over 1/4), followed by 8
> terms each larger than or equal to 1/32 (thus summing to over 1/4), etc.
> The sum is thus at least 1/4 + 1/4 + 1/4 + ..., which is clearly is
> infinite, so the series diverges.  This is probably the easiest way to see
> this, without appealing to integrals and the like.
>
>
> Laurent Hodges, Professor of Physics
> 12 Physics Hall, Iowa State University, Ames, IA  50011-3160
> lhodges@iastate.edu   http://www.public.iastate.edu/~lhodges