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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
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