Mathematica 9 is now available
Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
2005
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 2005

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

Search the Archive

Newbie Limit problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg53442] Newbie Limit problem
  • From: Ken Tozier <kentozier at comcast.net>
  • Date: Wed, 12 Jan 2005 03:41:12 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

I'm trying to get a limit for a sum that I know converges as s->infinity

\!\(Limit[\[Sum]\+\(k = 0\)\%s\((\(d\^2 + 2\ s\^2 - 2\ s\ \((s\ 
Cos[\(2\ \
\[Pi]\)\/s] + d\ \((Cos[\(2\ k\ \[Pi]\)\/s] - Cos[\(2\ \((1 + k)\)\ \
\[Pi]\)\/s])\))\)\)\/s\^2)\)\^0.5`, s \[Rule] \[Infinity]]\)

but all I'm getting for a result is the exact expression I plug into 
the Limit function.

\!\(Limit[\[Sum]\+\(k = 0\)\%s\((\(d\^2 + 2\ s\^2 - 2\ s\ \((s\ 
Cos[\(2\ \
\[Pi]\)\/s] + d\ \((Cos[\(2\ k\ \[Pi]\)\/s] - Cos[\(2\ \((1 + k)\)\ \
\[Pi]\)\/s])\))\)\)\/s\^2)\)\^0.5`, s \[Rule] \[Infinity]]\)

I read the documentation which describes this scenario like so: "Limit 
returns unevaluated when it encounters functions about which it has no 
specific information. Limit therefore by default makes no explicit 
assumptions about symbolic functions."

Next I tried to explicitly give it some assumptions like so:

\!\(Assuming[{s \[Element] Integers, d \[Element] Reals},
     Limit[\[Sum]\+\(k = 0\)\%s\((\(1\/s\^2\) \((d\^2 + 2\ s\^2 - 2\ s\ 
\((s\ \
Cos[\(2\ \[Pi]\)\/s] + d\ \((Cos[\(2\ k\ \[Pi]\)\/s] - Cos[\(2\ \((1 + 
k)\)\ \
\[Pi]\)\/s])\))\))\))\)\^0.5`, s \[Rule] \[Infinity]]]\)

which yields the same result.

\!\(Limit[\[Sum]\+\(k = 0\)\%s\((\(d\^2 + 2\ s\^2 - 2\ s\ \((s\ 
Cos[\(2\ \
\[Pi]\)\/s] + d\ \((Cos[\(2\ k\ \[Pi]\)\/s] - Cos[\(2\ \((1 + k)\)\ \
\[Pi]\)\/s])\))\)\)\/s\^2)\)\^0.5`, s \[Rule] \[Infinity]]\)

Am I using "Limit" wrong? Or is there some other way to write the 
expression to get Mathematica to give me the limit?

Thanks

Ken


  • Prev by Date: Take 2: MultipleListPlot MakeSymbol Issue
  • Next by Date: Re: [Newbie] Ohm, Ampere, Volt units
  • Previous by thread: Take 2: MultipleListPlot MakeSymbol Issue
  • Next by thread: Newbie Limit problem