A Theorem on the Binomial Coefficients of Combinatorial Geometric Series and Some Solutions on Partitions of the Binomial Coefficients

This paper presents a theorem on the binomial coefficients of combinatorial geometric series and its solutions for the binomial expression under the partitions of the binomial coefficients. The coefficient for each term in combinatorial geometric series refers to a binomial coefficient. These ideas can enable the scientific researchers to solve the real life problems.