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>