This paper focuses on the successive partition method applied to a binomial coefficient in combinatorial geometric series. 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...

Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and combinatorial equations for solving today’s scientific problems and challenges. This paper presents a new binomial expansion and theorem. This idea can enable scientific...

Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and combinatorial equations for solving today’s scientific problems and challenges. This paper presents a new multinomial expansion and theorem. This idea can enable the...

Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and combinatorial equations for solving today’s scientific problems and challenges. This paper presents the computation of binomial expansions in algorithmic way. These ideas can...

Nowadays, the growing complexity of mathematical and computational modelling demands the simplicity of mathematical and combinatorial equations for solving today’s scientific problems and challenges. This paper presents the two different and equal coefficients of combinatorial geometric series...

This paper presents lemmas and its corollaries on the combinatorial geometric series and summation of series of binomial coefficients. Also, the coefficient for each term in combinatorial geometric series refers to a binomial coefficient. These ideas can enable scientific researchers to solve...

This paper presents a multinomial theorem on the binomial coefficients for combinatorial geometric series. 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

This paper presents an innovative theorem using factorials, integers, and binomials and multinomials. The theorems and its results can be used as an application in computing and cryptography to develop algorithms like RSA algorithm and Elliptic Curve Cryptography

This paper presents the computing method for the derivative of geometric series without using the differentiation. This idea will be useful for researchers who are involving in finding the scientific solutions