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Harmonic Numbers

  • To: mathgroup at smc.vnet.net
  • Subject: [mg107881] Harmonic Numbers
  • From: "Chris H. Fleming" <chris_h_fleming at yahoo.com>
  • Date: Tue, 2 Mar 2010 03:34:31 -0500 (EST)

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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