Version 1
: Received: 13 July 2024 / Approved: 22 July 2024 / Online: 22 July 2024 (04:58:09 CEST)
How to cite:
Askari, A. D. I. F. Recursive Formula for Sum of Powers of Natural Numbers and Its Generalization to Arithmetic Progression. Preprints2024, 2024071648. https://doi.org/10.20944/preprints202407.1648.v1
Askari, A. D. I. F. Recursive Formula for Sum of Powers of Natural Numbers and Its Generalization to Arithmetic Progression. Preprints 2024, 2024071648. https://doi.org/10.20944/preprints202407.1648.v1
Askari, A. D. I. F. Recursive Formula for Sum of Powers of Natural Numbers and Its Generalization to Arithmetic Progression. Preprints2024, 2024071648. https://doi.org/10.20944/preprints202407.1648.v1
APA Style
Askari, A. D. I. F. (2024). Recursive Formula for Sum of Powers of Natural Numbers and Its Generalization to Arithmetic Progression. Preprints. https://doi.org/10.20944/preprints202407.1648.v1
Chicago/Turabian Style
Askari, A. D. I. F. 2024 "Recursive Formula for Sum of Powers of Natural Numbers and Its Generalization to Arithmetic Progression" Preprints. https://doi.org/10.20944/preprints202407.1648.v1
Abstract
In this paper, we derive a formula for sum of powers of integers from Abel’s Summation Formula. This formula enables us to generate the formula for the sum of k-th power of integers, denoted by Sk(n), given the formulas of S1(n), S2(n), ..., Sk−1(n). Furthermore, we shall extend this formula to compute the sum of powers of an arithmetic progression. Moreover, we can combine the formula with the result of Bernoulli to derive another result which enables us to find Bernoulli Numbers recursively.
Keywords
sum of powers; arithmetic progression; bernoulli numbers
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
