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real telescopic sum becomes complex?

• To: mathgroup at smc.vnet.net
• Subject: [mg54358] real telescopic sum becomes complex?
• From: Peter Pein <petsie at arcor.de>
• Date: Sat, 19 Feb 2005 02:32:02 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

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

• Follow-Ups:
  • Re: real telescopic sum becomes complex?
    • From: Chris Chiasson <chris.chiasson@gmail.com>
  • Re: real telescopic sum becomes complex?
    • From: DrBob <drbob@bigfoot.com>