       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//TextForm
telesum[n]//FullForm
%/.n\[Rule]5//TextForm
N[%]

{5.0 for Microsoft Windows (November 18, 2003),x86}
Sqrt
Plus[Times[-1,HarmonicNumber[Plus[-1,n],Rational[-1,2]]],
HarmonicNumber[n,Rational[-1,2]]]
Sqrt
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:=
>   {\$Version, \$ProcessorType}
> Out=
>   {"4.0 for Microsoft Windows (July 16, 1999)", "x86"}
> In:=
>   telesum[n_] := Sum[Sqrt[k] - Sqrt[k - 1], {k, 1, n}]
> In:=
>   telesum
> Out=
>   Sqrt
> OK - but:
> In:=
>   telesum[n]
> Out=
>   HarmonicNumber[n, -(1/2)] +
>    I*(Zeta[-(1/2)] - Zeta[-(1/2), 1 - n])
> In:=
>   % /. n -> 5
> Out=
>   3 + Sqrt + Sqrt + Sqrt +
>    I*(Zeta[-(1/2)] - Zeta[-(1/2), -4])
> In:=
>   N[%]
> Out=
>   8.382332347441762 - 6.146264369941973*I
>
>
> Has anyone got an explanation, what could have happened inside
> Mathematica to get this nonsense?
>
>   Peter
>
> --
> Peter Pein
> Berlin
>
>

--
Chris Chiasson
Kettering University
Mechanical Engineering