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Cubic Polynomial for the Series of Consecutive Cubes under Alternating Signs

Leomarich Fortugaliza Casinillo, Crisanto L Abas

Abstract


This paper aims to develop an elegant formula for the series of consecutive cubes of natural numbers under alternating signs. In addition, this paper investigates the formula under odd and even number of terms and discuss some important findings.

Keywords: Consecutive cubes; alternating signs; odd and even terms.

2010 Mathematics Subject Classification: 11B13, 11B50, 97I30


Abstrak

Paper ini bertujuan membangun formula yang elegan untuk deret berganti tanda bilangan-bilangan kubik berurutan.  Paper ini juga menyelidiki formula untuk banyak suku ganjil dan untuk banyak suku genap, dan mendiskusikan beberapa temuan penting.

Kata kunci:. Bilangan kubik berurutan, berganti tanda, suku ganjil dan suku genap


Keywords


consecutive cubes; alternating signs; odd and even terms

References


G. F. C. de Bruyn and J. M. de Villiers, "Formulas for 1^p+2^p+... +n^p.," The Fibonacci Quarterly, vol. 32, no. 3, pp. 271-276, 1994.

F. T. Howard , "Sums of powers of integers via generating functions," Fibonacci Quarterly, vol. 34, no. Retrieved from https://www.fq.math.ca/Scanned/34-3/howard.pdf, pp. 244-256, 1996.

D. Kalman, "Sums of Powers by Matrix Methods," The Fibonacci Quarterly, vol. 28, no. 1, pp. 60-71, 1990.

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

B. Turner, "Sums of Powers of Integers via the Binomial Theorem," Mathematics Magazine, vol. 53, pp. 92-96, 1980.

L. F. Casinillo and L. A. Mamolo, "Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs," InPrime: Indonesian Journal of Pure and Applied Mathematics, vol. 2, no. 2, pp. 91-96, 2020.


Full Text: PDF

DOI: 10.15408/inprime.v3i2.20116

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