On the sum of k-th powers of the first n positive integers

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ID: 286858
2023
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Abstract
One of the many functions that has been widely studied and is of interest to mathematicians due to its historic applications is the sum of powers of positive integers. This paper is expository in nature and is based mainly on the article โ€œOn the sum of ๐‘˜th powers in terms of earlier sumsโ€ by Steven J. Miller and Enrique Trevinฬƒo which appeared in The College Mathematics Journal (2020). For positive integer ๐‘› and nonnegative integer ๐‘˜, we let ๐‘†๐‘˜(๐‘›) = 1๐‘˜ + 2๐‘˜ + โ‹ฏ + ๐‘›๐‘˜. We will give an exposition of the proof of a classical result due to Blaise Pascal which gives the following recursive formula for the sum of powers. Miller and Treviรฑo improved Pascal's formula by proving that for positive integers ๐‘› and ๐‘˜, the sum of ๐‘˜th powers is a polynomial of the sum of 1st and 2nd powers. This paper aims to provide a better understanding of sums of powers of positive integers and contribute valuable insights for future work in this area.
Reference Key
persistent_1760659875_68f189a3010a3 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Alix, Arch Raphael Payang
Journal Malay Journal
Year 2023
DOI
DOI not found
URL
https://animorepository.dlsu.edu.ph/etdb_math/31
Keywords Keywords not found

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