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

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  • Subject: [mg8435] Re: [mg8344] Sum[1/(n^2 +n+1)^2,{n,1,p}]
  • From: Richard Gass <gass at>
  • Date: Sat, 30 Aug 1997 00:42:44 -0400
  • Sender: owner-wri-mathgroup at

 Wouter writes
>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
>although it obviously should.
>How about the new release?
I ran this on a Power Mac with 3.01 and had the same problem. If I set p->1
and attempt to get a numeric output I get Indeterminate as a result.

test=Sum[1/(n^2 +n+1)^2,{n,1,p}];
after many hours of runing on a 210MHz 604e I ran the kernel out of memory
have used 70Meg of physical ram and I got the following error message

  \(FactorSquareFreeList::"poly"\), \( : \ \),
    "\<"\!\(TraditionalForm\`\(2\\ \
\*TagBox[\(\\[CapitalPhi](\(\\[LeftSkeleton] 1 \\[RightSkeleton]\))\), \
InterpretTemplate[Function[LerchPhi[Slot[1], Slot[2], Slot[3]]]]]\\ \
\((\(\ at 3\\ \(Integrate`V(6)\)\^7\) - \(3\\ \\[ImaginaryI]\\ \
\(Integrate`V(6)\)\^7\) + \(\\[LeftSkeleton] 14 \\[RightSkeleton]\) + \(81\\ \
\\[ImaginaryI]\))\)\)\) is not a polynomial."\>"}], TraditionalForm]\)

I also tried Limit. This did nothing until I load the package Limit and
then it produced


    "Options expected (instead of \
\!\(TraditionalForm\`\(Calculus`Limit`Private`Simp(\(\(IncludeSingularTerm \
\\[Rule] False\), \(\(\\[LeftSkeleton] 31 \\[RightSkeleton]\) \\[Rule] 0\)\))\
\)\)) beyond position \!\(TraditionalForm\`2\) in \
\!\(TraditionalForm\`\(Zeta(\(2, \(\(\\[LeftSkeleton] 27 \\[RightSkeleton]\)(\
\(\\[LeftSkeleton] 1 \\[RightSkeleton]\))\), \(Calculus`Limit`Private`Simp(\(\
\\[LeftSkeleton] 1 \\[RightSkeleton]\))\)\))\)\). An option must be a rule or \
a list of rules."
and a host of similar error message before returning unevaluated.

Richard Gass
Department of Physics
University of Cincinnati
Cincinnati, OH 45221
phone- 513-556-0519
E-Mail gass at

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