Computational Techniques and Calculus for the Summation of Geometric Series and Binomial Expansions

This paper presents algorithmic techniques, computation, and differential and integral calculus for the summation of geometric series and binomial expansions in an innovative way and also theorems and relationship between the binomial expansions and geometric series. This computational technique refers to the methodological advance which is useful for researchers who are working in computational science. Computational science is a rapidly growing multi-and inter-disciplinary area where science, engineering, computation, mathematics, and collaboration use advance computing capabilities to understand and solve the most complex real life problems.