Athreya, K. B. ; Kothari, S.
(2015)
*Polynomial formula for sums of powers of integers*
Resonance, 20
(8).
pp. 726-743.
ISSN 0971-8044

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208kB |

Official URL: http://doi.org/10.1007/s12045-015-0229-9

Related URL: http://dx.doi.org/10.1007/s12045-015-0229-9

## Abstract

In this article, it is shown that for any positive integer k ≥ 1, there exist unique real numbers a kr , r= 1, 2,…, (k+1), such that for any integer n ≥ 1 Sk,n≡∑j=1njk=∑r=1(k+1)akrnr. The numbers a kr are computed explicitly for r = k + 1, k, k - 1,…, (k - 10). This fully determines the polynomials for k = 1, 2,…, 12. The cases k = 1, 2, 3 are well known and available in high school algebra books.

Item Type: | Article |
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Source: | Copyright of this article belongs to Springer Nature |

Keywords: | Sums of powers, integers, polynomial formula |

ID Code: | 131562 |

Deposited On: | 07 Dec 2022 06:12 |

Last Modified: | 07 Dec 2022 06:12 |

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