Re: real telescopic sum becomes complex?

• To: mathgroup at smc.vnet.net
• Subject: [mg54423] Re: real telescopic sum becomes complex?
• 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]
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```

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