Author(s): Songbai GUO, Youjian SHEN, School of Mathematics and Statistics, Hainan Normal University, School of Mathematics and Physics, University of Science and Technology Beijing
Pages: 666-672
Year: 2013 Issue:  6
Journal: Journal of Mathematical Research and Exposition
Keyword:  odd number; sums of powers; binomial theorem; superposition method;
Abstract: In this paper,by using superposition method,we aim to show thatn i=1(2i 1)2k 1 is the product of n2and a rational polynomial in n2with degree k 1,and thatn i=1(2i 1)2k is the product of n(2n 1)(2n + 1) and a rational polynomial in(2n 1)(2n + 1) with degree k 1.Moreover,recurrence formulas to compute the coefcients of the corresponding rational polynomials are also obtained.