A Simple Proof 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 statistical scientists in particular. Its proofs and applications appear quite often in textbooks of probability and mathematical statistics. In this article, a new and very simple proof of the binomial theorem is presented. The new proof is based on a direct computation involving partial derivatives.

KEY WORDS::

• Binomial distribution
• Combinatorial analysis
• Mathematical induction
• Multinomial theorem
• Partial derivatives