Joshi, Kapil D
(2018)
The power triangle.
At Right Angles, 7 (1).
pp. 3337.
Abstract
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 kth
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.
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