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Newbie Limit problem

• To: mathgroup at smc.vnet.net
• Subject: [mg53439] Newbie Limit problem
• From: Ken Tozier <kentozier at comcast.net>
• Date: Wed, 12 Jan 2005 03:41:09 -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

• Follow-Ups:
  • Re: Newbie Limit problem
    • From: Andrzej Kozlowski <akozlowski@gmail.com>