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

**References**:**real telescopic sum becomes complex?***From:*Peter Pein <petsie@arcor.de>