In is described for finding a formula for the sum of the powers of the first the companion article by Prof V G Tikekar, a method n positive integers, for any positive k-th
integer k, using a triangular array of numbers—the Power
Triangle. This article shows why the method works. The
proof makes use of a family of combinatorial numbers called
the Stirling set numbers (also called Stirling numbers of the second kind; they are dwelt upon in the other companion
article by Dr Shailesh Shirali). By exploiting a relation
between these numbers and the power functions, we are led
to the formulas we seek
