Re: real telescopic sum becomes complex?

*To*: mathgroup at smc.vnet.net*Subject*: [mg54423] Re: real telescopic sum becomes complex?*From*: Bill Rowe <readnewsciv at earthlink.net>*Date*: Sun, 20 Feb 2005 00:09:28 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

On 2/19/05 at 2:32 AM, petsie at arcor.de (Peter Pein) wrote: >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, $ProcessorType} >Out[1]= >{"4.0 for Microsoft Windows (July 16, 1999)", "x86"} >In[2]:= >telesum[n_] := Sum[Sqrt[k] - Sqrt[k - 1], {k, 1, n}] >In[3]:= >telesum[5] >Out[3]= >Sqrt[5] >OK - but: In[4]:= >telesum[n] >Out[4]= >HarmonicNumber[n, -(1/2)] + I*(Zeta[-(1/2)] - Zeta[-(1/2), 1 - n]) >In[5]:= >% /. n -> 5 >Out[5]= >3 + Sqrt[2] + Sqrt[3] + Sqrt[5] + I*(Zeta[-(1/2)] - Zeta[-(1/2), >-4]) This has apparently been corrected since In[1]:= {$Version, $ProcessorType} Out[1]= {"5.1 for Mac OS X (October 25, 2004)", "PowerPC"} In[2]:= telesum[n_] := Sum[Sqrt[k] - Sqrt[k - 1], {k, 1, n}] In[3]:= telesum[5] Out[3]= Sqrt[5] In[4]:= telesum[n] Out[4]= HarmonicNumber[n, -(1/2)] - HarmonicNumber[n - 1, -(1/2)] In[5]:= % /. n -> 5 Out[5]= Sqrt[5] -- To reply via email subtract one hundred and four