A simple tool for engineers for generating formulae for the sum of powers of natural numbers

摘要

The formulae for the sum of powers of natural numbers are in the form of polynomials. These formulae are derived using an algorithm which was developed from a simple geometric interpretation. It has been found that these polynomials are interdependent. In this paper, a close study is made and many interesting features are brought out. A method is proposed to generate a new polynomial based on the features of these polynomials. Another simplified algorithm is also presented which is found to be more suitable for the automatic generation of the polynomials. The latter may be realized as a convenient and handy tool for generating the formulae, especially for engineers.