Re: Harmonic Numbers
- To: mathgroup at smc.vnet.net
- Subject: [mg107914] Re: Harmonic Numbers
- From: "Chris H. Fleming" <chris_h_fleming at yahoo.com>
- Date: Tue, 2 Mar 2010 07:55:28 -0500 (EST)
- References: <hmikua$54l$1@smc.vnet.net>
On Mar 2, 4:14 am, "Chris H. Fleming" <chris_h_flem... at yahoo.com>
wrote:
> 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?
Everyone else was getting the right answer, so I went back through my
file to look for the culprit.
I have found the problem.
$Assumptions = {k > 0};
Sum[k/((k^2 + 1) (k^2 + 4)), {k, 1, \[Infinity]}]
Sum does not converge.
I had required k>0 to get to this point (convergent integrals) but
didn't imagine that it would have any effect on this sum.
Strangely a numerator of k^0 or k^2 will work, just not k^1.