NOVEL WAY OF DETERMINING SUM OF KTH POWERS OF NATURAL NUMBERS

Authors

  • V.R. Kalyan Kumar Independent Research Scholar, California Public University, USA
  • Dr. R. Sivaraman Associate Professor, Post Graduate and Research Department of Mathematics, Dwaraka Doss Goverdhan Doss Vaishnav College, Arumbakkam, Chennai, India

DOI:

https://doi.org/10.29121/granthaalayah.v12.i1.2024.5491

Keywords:

Sum of Kth Powers of Natural Numbers, Differentiation, Bernoulli Numbers, Faulhaber’s Triangle

Abstract [English]

Since ancient times, mathematicians across the world have worked on different methods to find the sum of powers of natural numbers. In this paper, we are going to present the relationship between sum of kth powers of natural numbers and sum of (k–1) th powers of natural numbers using the differential operator and associated recurrence relation. Interestingly, the Bernoulli numbers which occur frequently in mathematical analysis, play an important role in establishing this relationship.

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References

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Published

2024-02-06

How to Cite

Kumar, V. K., & Sivaraman, R. (2024). NOVEL WAY OF DETERMINING SUM OF KTH POWERS OF NATURAL NUMBERS. International Journal of Research -GRANTHAALAYAH, 12(1), 49–54. https://doi.org/10.29121/granthaalayah.v12.i1.2024.5491