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

This paper presents the summations and sums of Single terms and successive terms of geometric series with negative exponents (negative powers). This idea will be useful for researchers who are involving in solving the scientific problems

This paper presents the summations of single terms and successive terms of geometric series and computation of the first derivative of geometric series in a different way. This idea will be useful for researchers who are involving in finding the scientific solutions

This paper presents an algorithmic technique to establish a theorem on the Annamalai’s binomial identities. The binomial theorem and its computing technique refer to a sort of methodological advances that is useful for researchers working in computation, science, engineering, and management

This paper present computation of the summation of geometric series in an innovative way. Geometric series is a computational method which is used for numerous applications in science, engineering, and medicine. The geometric series and exponential decay model have already been used as...

This paper presents the summations of binomial expansions with the optimized binomial coefficients and also the sum of multiple summations of the binomial coefficients. This combinatorial result is useful for researchers who are working in computing, science, engineering, and management

The optimized binomial coefficient or binomial expansion has been derived from the multiple summations of geometric series. This binomial coefficient is a methodological advance in the areas of combinatorics and theoretical computer science. This paper presents a new theorem with binomial...

This paper presents an extended definition of intuitionistic fuzzy set and some operations on intuitionistic fuzzy sets which will be very useful for solving the real life problems. In fact, the intuitionistic fuzzy set is an extension of the fuzzy set defined in a domain of discourse. In this...