Sum of Powers of Natural Numbers: A Simple Approach by a Mechanical Engineer

摘要

Convenient formulae for finding the sums of Kth power of first n natural numbers may be useful in some engineering applications. The formulae for k = 1, 2 and 3, are commonly found in the literature. In this paper, an attempt is made to develop a general algorithm for finding the sum for any positive integer value of k. The development of the algorithm is entirely an engineering approach, purely basing on a simple geometric interpretation and does not involve any deep mathematics. This algorithm may be used to derive the formulae for different values of k.