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Re: Sum[1/(n^2 +n+1)^2,{n,1,p}]

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  • Subject: [mg8428] Re: [mg8344] Sum[1/(n^2 +n+1)^2,{n,1,p}]
  • From: seanross at
  • Date: Sat, 30 Aug 1997 00:42:37 -0400
  • Sender: owner-wri-mathgroup at

w.meeussen wrote:
> a small request to those having Mma 3.0.1. :
> in my Mma 3.0.0. (Win'95)
> the symbolic sum
>  Sum[1/(n^2 +n+1)^2,{n,1,p}]
> works out to a    v e r y   impressive symbolic expression.
> But, setting p->1 or (any other integer) on the result yields no numeric output,
> although it obviously should.
> How about the new release?
> wouter.
> Dr. Wouter L. J. MEEUSSEN
> eu000949 at
> w.meeussen.vdmcc at

On my Win95 pentium with Mma 3.0.1, 
Sum[1/(n^2 + n +1),{n,1,p}] returns a sum in terms of Polygamma and Tanh

Sum[1/(n^2 + n +1),{n,1,3}] returns a fraction 151/273.  

Sum[1/(n^2 + n +1)^2,{n,1,p}] returns a huge symbolic solution in terms
of LerchPhi and Zeta functions.

Sum[1/(n^2 + n +1)^2,{n,1,3}] returns a fraction

Sorry about the bug.  I was told that there is a patch for Mma 3.0.0 by
the folks at Wolfram.  You'll need to call them up to get it.  I hope it
fixes the problem.  Have you tried N[Sum[...?

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