Novel Finite Sum Identities Involving Reciprocals of Binomial Coefficients

Finite sums involving reciprocals of binomial coefficients have long intrigued mathematicians, owing to their elegant structure and unexpected identities. In this work, we present a comprehensive general formula that unifies and extends several results previously studied in the literature. To demonstrate the breadth and utility of our approach, we also investigate a variety of significant special cases, shedding light on deeper patterns and connections. This unified perspective aims to appeal to researchers interested in combinatorics, number theory, and special functions.