SUMS OF POWERS WITH Fk NUMBERS
We present a slightly different formula for the sums of powers, known as Bernoulli’s formula. In literature, this formula is written using Bernoulli numbers, however, in this paper, we suggest the implementation of Fk numbers instead. The method of obtaining the aforementioned formula is new and this novel approach can be deemed as more natural. We show that the introduction of the sequence Fk is justified by a large number of examples where it can be seen that in applications, it is used exactly through the sequence Fk while Bernoulli's sequence Bk always requires division with k.
sums of powers, Bernoulli’s numbers, Fk numbers.
Received: March 7, 2021; Accepted: April 24, 2021; Published: June 28, 2021
How to cite this article: Aleksa Srdanov, Radiša Stefanović and Nada Ratković Kovačević, Sums of powers with Fk numbers, JP Journal of Algebra, Number Theory and Applications 51(1) (2021), 77-95. DOI: 10.17654/NT051010077
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
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