Re: real telescopic sum becomes complex?

• To: mathgroup at smc.vnet.net
• Subject: [mg54449] Re: [mg54358] real telescopic sum becomes complex?
• From: DrBob <drbob at bigfoot.com>
• Date: Sun, 20 Feb 2005 00:10:58 -0500 (EST)
• References: <200502190732.CAA06051@smc.vnet.net>
• Reply-to: drbob at bigfoot.com
• Sender: owner-wri-mathgroup at wolfram.com

```Version 5.1 does somewhat better:

telesum[n_] := Sum[Sqrt[k] - Sqrt[k - 1], {k, 1, n}]
telesum[5]
telesum[n]
% /. n -> 5

Sqrt[5]
-HarmonicNumber[-1 + n, -(1/2)] + HarmonicNumber[n, -(1/2)]
Sqrt[5]

Sum still makes plenty of mistakes, so always sanity-check the results.

Bobby

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
>

--
DrBob at bigfoot.com
www.eclecticdreams.net

```

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