Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs

Authors

  • Leomarich F Casinillo Visayas State University
  • Leo A Mamolo Visayas State University

DOI:

https://doi.org/10.15408/inprime.v2i2.15845

Keywords:

consecutive -squares, alternating signs, odd and even terms.

Abstract

Abstract

This paper developed a simple but elegant formula for the series of consecutive square of natural numbers under alternating signs. Furthermore, this study investigated the said formula under odd and even number of terms and discuss some important results.

Keywords: consecutive -squares; alternating signs; odd and even terms.

 

Abstrak

Dalam paper ini kita membangun formula yang sederhana namun elegan untuk menghitung jumlah deret berganti-tanda dari kuadrat bilangan-bilangan asli berurutan.  Kita akan menyelidiki formula untuk kasus banyaknya suku ganjil maupun genap dan mendiskusikan beberapa hasil yang penting.

Kata kunci: -kuadrat berurutan; berganti-tanda; bersuku ganjil dan bersuku genap.

References

R. P. Bambah and S. Chowla, "On numbers which can be express as a sum of two squares.," Pro. Nat. Acad. Sci. India, vol. 13, pp. 101-103, 1947.

G. Harman, "Sums of two squares in short intervals," Proceeding of London Mathematical Society, vol. 6, pp. 225-241, 1991.

F. T. Howard , "Sums of powers of integers via generating functions," Fibonacci Quarterly, vol. 34, pp. 244-256, 1996. Retrieved from https://www.fq.math.ca/Scanned/34-3/howard.pdf.

M. Merca, "An alternative to Faulhaber’s formula," The American Mathematical Monthly, vol. 122, no. 6, pp. 599-601, 2014. DOI: 10.4169/amer.math.monthly.122.6.599.

M. Marin, "Contributions on Uniqueness in thermoelastodynamics on bodies with voids," Ciencias Mathematicas (Havana), vol. 16, no. 2, pp. 101-109, 1998.

M. Marin, "An evolutionary equation in thermoelasticity of dipolar bodies," Journal of Mathematical Physics, vol. 40, no. 3, pp. 1391-1399, 1999.

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Published

2020-06-24

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Section

Articles

How to Cite

Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs. (2020). InPrime: Indonesian Journal of Pure and Applied Mathematics, 2(2), 91-96. https://doi.org/10.15408/inprime.v2i2.15845