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MathGroup Archive 2005

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Problem with a sum

  • To: mathgroup at
  • Subject: [mg53878] Problem with a sum
  • From: ncc1701zzz at
  • Date: Tue, 1 Feb 2005 04:08:32 -0500 (EST)
  • Sender: owner-wri-mathgroup at


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

Thanks a lot for your help.

Best regards.

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