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