Re: Problem with a sum

*To*: mathgroup at smc.vnet.net*Subject*: [mg53890] Re: [mg53878] Problem with a sum*From*: DrBob <drbob at bigfoot.com>*Date*: Wed, 2 Feb 2005 06:25:53 -0500 (EST)*References*: <200502010908.EAA15067@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Well, it seems to me that you already know what to do. Here's a function that does it, if that helps: Clear@f f[Infinity] = NSum[(k^2 - (1/2))/(k^4 + (1/4)), {k, 1, Infinity}]; f[m_?NumericQ] := Sum[(k^2 - (1/2))/(k^4 + (1/4)), {k, 1, m}] f /@ Range@20 {2/5, 8/13, 18/25, 32/41, 50/61, 72/85, 98/113, 128/145, 162/181, 200/221, 242/265, 288/313, 338/365, 392/421, 450/481, 512/545, 578/613, 648/685, 722/761, 800/841} f@Infinity 1. > I have no problems with the sum in that form, but... I'm not sure why you'd say that, if the result isn't correct when a value is substituted for m. The symbolic form of the sum may be valid for SOME values of n, on the other hand, but I don't think I'd bother trying to debug it. Bobby On Tue, 1 Feb 2005 04:08:32 -0500 (EST), <ncc1701zzz at hotmail.com> wrote: > 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. > > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**Problem with a sum***From:*ncc1701zzz@hotmail.com

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