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
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