In this paper, we first quickly review the basics of an algebro-geometric method of Karaji's L-summing technique in today's modern language of algebra. Then, we also review the theory of Gosper's algorithm as a decision procedure for obtaining the indefinite sums involving hypergeometric terms. Then, we show that how one can use Gosper's algorithm equipped with the L-summing method to obtain a class of combinatorial identities associated with a given algebraic identity.