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MathGroup Archive 2005

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Re: real telescopic sum becomes complex?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg54442] Re: [mg54358] real telescopic sum becomes complex?
  • From: Chris Chiasson <chris.chiasson at gmail.com>
  • Date: Sun, 20 Feb 2005 00:10:30 -0500 (EST)
  • References: <200502190732.CAA06051@smc.vnet.net>
  • Reply-to: Chris Chiasson <chris.chiasson at gmail.com>
  • Sender: owner-wri-mathgroup at wolfram.com

{$Version,$ProcessorType}
telesum[n_]:=Sum[Sqrt[k]-Sqrt[k-1],{k,1,n}]
telesum[5]//TextForm
telesum[n]//FullForm
%/.n\[Rule]5//TextForm
N[%]

{5.0 for Microsoft Windows (November 18, 2003),x86}
Sqrt[5]
Plus[Times[-1,HarmonicNumber[Plus[-1,n],Rational[-1,2]]],
  HarmonicNumber[n,Rational[-1,2]]]
Sqrt[5]
2.23607

On Sat, 19 Feb 2005 02:32:02 -0500 (EST), Peter Pein <petsie at arcor.de> wrote:
> Dear Group,
> 
> I'v only got the old version 4.0 of Mathematica and I would like to know
> whether later versions do the same mistake:
> 
> In[1]:=
>   {$Version, $ProcessorType}
> Out[1]=
>   {"4.0 for Microsoft Windows (July 16, 1999)", "x86"}
> In[2]:=
>   telesum[n_] := Sum[Sqrt[k] - Sqrt[k - 1], {k, 1, n}]
> In[3]:=
>   telesum[5]
> Out[3]=
>   Sqrt[5]
> OK - but:
> In[4]:=
>   telesum[n]
> Out[4]=
>   HarmonicNumber[n, -(1/2)] +
>    I*(Zeta[-(1/2)] - Zeta[-(1/2), 1 - n])
> In[5]:=
>   % /. n -> 5
> Out[5]=
>   3 + Sqrt[2] + Sqrt[3] + Sqrt[5] +
>    I*(Zeta[-(1/2)] - Zeta[-(1/2), -4])
> In[6]:=
>   N[%]
> Out[6]=
>   8.382332347441762 - 6.146264369941973*I
> 
> (please note, that Re[%]+Im[%]==Sqrt[5.]!!!)
> 
> Has anyone got an explanation, what could have happened inside
> Mathematica to get this nonsense?
> 
> Thanks in advance,
>   Peter
> 
> --
> Peter Pein
> Berlin
> 
> 


-- 
Chris Chiasson
Kettering University
Mechanical Engineering
Graduate Student
1 810 265 3161


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