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Abstract
This paper presents a computing method for the sum of summation of geometric series and the summation of series of binomial expansions in an innovative way. Geometric Series plays a vital role in the field of combinatorics including binomial coefficients. The multiple summations of series of binomial coefficients or computation of multiple binomial expansions are equal to the exponents of two. These methodological advances are useful for the researchers who are working in science, engineering, economics, computation, and management.
