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From: leigh pascoe on 2 Mar 2010 08:01
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

From: leigh pascoe on 3 Mar 2010 05:54
Le 02/03/2010 13:56, leigh pascoe a =C3=A9crit :
> 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
>
>
>
Correction of previous reply
In[16]:= $Version
Out[16]= 7.0 for Microsoft Windows (32-bit) (February 18, 2009)

In[17]:= NSum[k/((k^2+1) (k^2+4)),{k,1,\[Infinity]}]
Out[17]= 0.206647

In[18]:= Sum[k/((k^2 + 1) (k^2 + 4)), {k, 1, \[Infinity]}]
Out[18]= -(1/2) RootSum[10 + 14 #1 + 11 #1^2 + 4 #1^3 + #1^4 &,
PolyGamma[0, -#1]/(7 + 4 #1 + 2 #1^2) &]

In[19]:= N[%]
Out[19]= 0.206647 + 0. I



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