Re: real telescopic sum becomes complex?

*To*: mathgroup at smc.vnet.net*Subject*: [mg54408] Re: [mg54358] real telescopic sum becomes complex?*From*: Bob Hanlon <hanlonr at cox.net>*Date*: Sun, 20 Feb 2005 00:08:13 -0500 (EST)*Reply-to*: hanlonr at cox.net*Sender*: owner-wri-mathgroup at wolfram.com

$Version 5.1 for Mac OS X (October 25, 2004) telesum[n_]:=Sum[Sqrt[k]-Sqrt[k-1],{k,1,n}]; Table[telesum[n],{n,10}] {1, Sqrt[2], Sqrt[3], 2, Sqrt[5], Sqrt[6], Sqrt[7], 2*Sqrt[2], 3, Sqrt[10]} telesum[n] HarmonicNumber[n, -(1/2)] - HarmonicNumber[n - 1, -(1/2)] %/.n->Range[10] {1, Sqrt[2], Sqrt[3], 2, Sqrt[5], Sqrt[6], Sqrt[7], 2*Sqrt[2], 3, Sqrt[10]} Bob Hanlon > > From: Peter Pein <petsie at arcor.de> To: mathgroup at smc.vnet.net > Date: 2005/02/19 Sat AM 02:32:02 EST > To: mathgroup at smc.vnet.net > Subject: [mg54408] [mg54358] real telescopic sum becomes complex? > > Dear Group, > > I'v only got the old version 4.0 of Mathematica and I would like to know > whether later versions do the same mistake: > > In[1]:= > {$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 > >