  Recently, Chen, Hou and Jin used both Abel's lemma on summation by parts and
Zeilberger's algorithm to generate recurrence relations for definite
summations. Meanwhile, they proposed the Abel-Gosper method to evaluate some
indefinite sums involving harmonic numbers. In this paper, we use the
Abel-Gosper method to prove an identity involving the generalized harmonic
numbers. Special cases of this result reduce to many famous identities. In
addition, we use both Abel's lemma and the WZ method to verify and to discover
identities involving harmonic numbers. Many interesting examples are also
presented.
