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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
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