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ANOTHER LOOK AT A POLYNOMIAL SOLUTION FOR ALTERNATING POWER SUMS

*Leomarich F Casinillo  -  Visayas State University, Philippines

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Abstract

This paper aims to provide a new general explicit polynomial solution on power sums of consecutive positive integers under alternating signs. Moreover, it examines the solution under odd and even number of terms in the series and provides some examples.

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Keywords: General polynomial, power sums; alternating signs; odd and even terms

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  1. Casinillo, L. F. (2021). Quadratic polynomial of power sums and alternating power sums. Journal of Fundamental Mathematics and Applications (JFMA), 4(2), 147-153
  2. Bazsó, A. (2015). Polynomial values of (alternating) power sums. Acta Mathematica Hungarica, 146(1), 202-219
  3. Merca, M. (2015). An alternative to Faulhaber's formula. The American Mathematical Monthly, 122(6), 599-601
  4. Howard, F. T. (1996). Sums of powers of integers via generating functions. Fibonacci Quarterly, 34, 244-256
  5. Casinillo, L. F., & Mamolo, L. A. (2020). Alternative Formula for the Series of Consecutive m-Squares under Alternating Signs. InPrime: Indonesian Journal of Pure and Applied Mathematics, 2(2), 91-96
  6. Casinillo, L. F., & Abas, C. L. (2021). Cubic Polynomial for the Series of Consecutive Cubes under Alternating Signs. InPrime: Indonesian Journal of Pure and Applied Mathematics, 3(2), 86-91

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