Any Isolated Number Belongs to a Certain Binomial Series

Abstract

A binomial is an algebraic expression with two dissimilar terms connected by +ve or -ve sign. Binomial Theorem is a way of expanding a binomial expression (that are raised to) large powers. According to Newton's binomial theorem power of any algebraic expression can be expanded in many terms. But so far, it has not been tried to generate a whole binomial theorem or Binomial expression from an isolated single numbers. The reverse is done by me with two pairs of mathematical formulas, i.e., two pairs of formulas have been developed to generate Binomial series/expression from any isolated single given number. Before using these formulas it is needed to arrange the isolated number as a binomial term with single variable or two variables. These generated Binomials have many applications in permutation and combination, probability, Matrices and Mathematical Induction also. So, existing given Binomials and here generated Binomials are two different processes, but both are same and have same applications and importance in algebra.