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Recently, Chen, Hou and Jin used both Abel's lemma on summation by parts andZeilberger's algorithm to generate recurrence relations for definitesummations. Meanwhile, they proposed the Abel-Gosper method to evaluate someindefinite sums involving harmonic numbers. In this paper, we use theAbel-Gosper method to prove an identity involving the generalized harmonicnumbers. Special cases of this result reduce to many famous identities. Inaddition, we use both Abel's lemma and the WZ method to verify and to discoveridentities involving harmonic numbers. Many interesting examples are alsopresented.

Abel's Lemma and Identities on Harmonic Numbers