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Re: Harmonic Numbers

• To: mathgroup at smc.vnet.net
• Subject: [mg107919] Re: [mg107881] Harmonic Numbers
• From: leigh pascoe <leigh at evry.inserm.fr>
• Date: Tue, 2 Mar 2010 07:56:29 -0500 (EST)
• References: <201003020834.DAA03875@smc.vnet.net>

Le 02/03/2010 09:34, Chris H. Fleming a =C3=A9crit :
> Sum[k/((k^2 + 1) (k^2 + 4)), {k, 1, \[Infinity]}]
>
> Sum does not converge.
>
> NSum[k/((k^2 + 1) (k^2 + 4)), {k, 1, \[Infinity]}]
>
> 0.206647
>
>
> Fortunately I know how to do this sum by hand, but Mathematica can
> usually handle these Harmonic number functions pretty well.
>
> Does anyone know a way of massaging this into a form Mathematica can
> digest?
>
>
>   
Mathematica 7.0.1.0
In[3]:= NSum[k/((k^2+1) (k^4+4)),{k,1,\[Infinity]}]
Out[3]= 0.125
In[4]:= Sum[k/((k^2+1) (k^4+4)),{k,1,\[Infinity]}]
Out[4]= 1/8

Leigh

• Follow-Ups:
  • Re: Re: Harmonic Numbers
    • From: leigh pascoe <leigh@evry.inserm.fr>

• References:
  • Harmonic Numbers
    • From: "Chris H. Fleming" <chris_h_fleming@yahoo.com>