Representation of One as the Sum of Unit Fractions

TL;DR

This paper presents an elegant proof that demonstrates how the number one can be represented as a sum of reciprocals of specific integers, utilizing polynomial theorems and basic calculus techniques.

Contribution

It provides a novel, elegant proof of representing one as a sum of unit fractions using polynomial theorem and calculus, enhancing understanding of Egyptian fractions.

Findings

Proof applies polynomial theorem and calculus

Representation of one as sum of unit fractions established

Provides an elegant mathematical proof

Abstract

One is expressed as the sum of the reciprocals of a certain set of integers. We give an elegant proof to the fact applying the polynomial theorem and basic calculus.