In this paper, we present an alternative proof for a generalization of a binomial identity by Simons, initially proven by Munarini. Unlike previous proofs, our approach uses the Taylor theorem and the Wilf-Zeilberger algorithm. We also offer a new binomial sum identity and generalize a combinatorial identity by Alzer and Kouba. Additionally, we derive several harmonic number identities, including the proof for H_n and a formula involving the square of binomial coefficients and harmonic numbers.