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Re: Harmonic Numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg107915] Re: [mg107881] Harmonic Numbers
  • From: Patrick Scheibe <pscheibe at trm.uni-leipzig.de>
  • Date: Tue, 2 Mar 2010 07:55:41 -0500 (EST)
  • References: <201003020834.DAA03875@smc.vnet.net>

Hi,

no problems here (OSX, Math 7)

In[5]:= Sum[k/((k^2+1) (k^2+4)),{k,1,\[Infinity]}]//FullSimplify

Out[5]= 1/6 (-HarmonicNumber[-I]-HarmonicNumber[I]+HarmonicNumber[-2 I] 
+HarmonicNumber[2 I])

In[6]:= %//N
Out[6]= 0.206647+0. I

Cheers
Patrick

Am Mar 2, 2010 um 9:34 AM schrieb Chris H. Fleming:

> 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?
>



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