Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Misbehaving Sum[..,{n,0,Infinity}]

• To: mathgroup at smc.vnet.net
• Subject: [mg37676] Misbehaving Sum[..,{n,0,Infinity}]
• From: "David M. Wood" <dmwood at slate.Mines.EDU>
• Date: Fri, 8 Nov 2002 02:15:27 -0500 (EST)
• Organization: Colorado School of Mines
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: Misbehaving Sum[..,{n,0,Infinity}]
    • From: Daniel Lichtblau <danl@wolfram.com>