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

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  • Subject: [mg8424] RE: [mg8344] Sum[1/(n^2 +n+1)^2,{n,1,p}]
  • From: "Richard W. Finley, M. D." <trfin at>
  • Date: Sat, 30 Aug 1997 00:42:32 -0400
  • Sender: owner-wri-mathgroup at


I have Mma 3.0.1 but I haven't installed it yet so I can't answer your =
question, but I did notice the interesting fact that the LARGE symbolic =
expression given when Mma 3.0 evaluates your sum contains a large number =
of evaluations of the LerchPhi function ( LerchPhi[z,s,a] ). These are =
the reason that the expression yields no numerical output because each =
one evaluates to infinity for z =3D 1, s =3D 1 for all a.  =
Interestingly, however, if you take all the terms involving the LerchPhi =
function and simplify, play around a bit, PowerExpand, they evaluate to =
ZERO.  The remaining terms involving the Zeta function can then also be =
simplified and when supplied with p->1 give .111111... or 1/9 as they =
should!  One could be a cynic and be disappointed that Mma didn't do the =
simplification to begin with, but I was impressed that one could =
simplify that horrible equation so easily.


-----Original Message-----
From:	w.meeussen [SMTP:meeussen.vdmcc at]
To: mathgroup at
Sent:	Tuesday, August 26, 1997 1:23 AM
To:	mathgroup at
Subject:	[mg8344] Sum[1/(n^2 +n+1)^2,{n,1,p}]=20

a small request to those having Mma 3.0.1. :

in my Mma 3.0.0. (Win'95)
the symbolic sum=20
 Sum[1/(n^2 +n+1)^2,{n,1,p}]=20
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?


Dr. Wouter L. J. MEEUSSEN
eu000949 at
w.meeussen.vdmcc at

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