Re: Misbehaving Sum[..,{n,0,Infinity}]
- To: mathgroup at smc.vnet.net
- Subject: [mg37704] Re: Misbehaving Sum[..,{n,0,Infinity}]
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Sat, 9 Nov 2002 00:29:08 -0500 (EST)
- Organization: Universitaet Leipzig
- References: <aqfpcb$7e1$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
in a finite sum the index is replaced by the numerical
value and all results of the evaluation of the sum-argument
with arg /. n->i are added.
In a infinite sum the index is handled symbolical and
so Sum[] can not find out that some of your If[] tests
would give True because mathematica can't insert a infinite
number of n's in a finite time to find all cases
where a If[Mod[n,2]==0,__] would give True.
Regards
Jens
"David M. Wood" wrote:
>
> Aaaargh.
>
> What is with Mathematica (4.2 here) and infinite sums?! (The
> following has annoyed me for years. I'm finally indignant enough to
> pose this query.)
>
> A nominally infinite sum for which only a finite number of terms
> contribute FAILS to evaluate for an uppper index limit of Infinity,
> but evaluates PROPERLY for an (arbitrary) finite upper index limit.
>
> Example:
>
> cn = If[n == 0, 1, 0] - 1/2 If[n == 1, 1, 0];
> Sum[x^(n-1) cn,{n,0,Infinity}]
>
> gives
>
> If[n == 0, 1, 0] - 1/2 If[n == 1, 1, 0]/((1 - x) x)
>
> while
>
> Sum[x^(n-1) cn,{n,0,731}]
>
> gives
>
> -1/2 + 1/x
>
> (which is, of course, what I want). I've Google-searched to no avail,
> nested Evaluate every which way, but only a finite upper limit works
> properly--inconvenient for formal results.
>
> Can anybody explain what's going on, or how to coerce Mathematica into not
> choking on an infinite number of non-contributing terms?
>
> Thanks!
>
> David M. Wood, Department of Physics, Colorado School of Mines,
> Golden, CO 80401; Phone: (303) 273-3853; Fax: (303) 273-3919
> http://www.mines.edu/Academic/physics/people/pages/wood.html
>
> --
> David M. Wood, Dept. of Physics, Colorado School of Mines, Golden, CO 80401
> Phone: (303) 273-3853; Fax: (303) 273-3919; e-mail: dmwood at Mines.EDU