A Simple Proof of the Generalization of the Binomial Theorem Using Differential Calculus

Abstract

The binomial theorem is a simple and important mathematical result, and it is of substantial interest to statisticalscientists in particular. Its proof and applications appear quite often in textbooks of probability and mathematicalstatistics. In this article, a new and very simple proof of multinomial theorem is presented. The new proof isbased on a direct computation involving partial derivatives.

Key Words: Binomial distribution; Combinatorial Analysis; Mathematical Induction; Multinomial theorem;Partial derivatives.