Problem with a sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg53878] Problem with a sum*From*: ncc1701zzz at hotmail.com*Date*: Tue, 1 Feb 2005 04:08:32 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello. I would like to ask you a question about a sum in a problem I have found in Mathematica 5.1. The sum is the following: Sum[(k^2 - (1/2))/(k^4 + (1/4)), {k, 1, 1000}] I have no problems with the sum in that form, but the following one doesn't work: s=Sum[(k^2 - (1/2))/(k^4 + (1/4)), {k, 1, m}] s /. m->1000 It gives a long result with hypergeometric functions. Also, it cannot be converted to a number with N[], due to some kind of ComplexInfinity problem. FullSimplify doesn't help, neither. Also, if I evaluate it to Infinity, I cannot get the value symbolically nor numerically, except if I use NSum[], that gives me the right result, 1. I don't know if I'm doing something wrong, it is a bug, a limitation or whatever. Thanks a lot for your help. Best regards.

**Follow-Ups**:**Re: Problem with a sum***From:*DrBob <drbob@bigfoot.com>