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