Thursday, 12 December 2013

calculus - A series involving the harmonic numbers : suminftyn=1fracHnn3

Let Hn be the nth harmonic number defined by Hn:=nk=11k.



How would you prove that



n=1Hnn3=π472?






Simply replacing Hn with nk=11k does not seem like a good starting point. Perhaps another representation of the nth harmonic number would be more useful.

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