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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
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