CAJ | 학술논문

通过若干初等函数的幂级数展开式及其变形,给出了用其他方法难以证明的条件数列和的代数恒等式,并给出了证明,其中二次s项数列和的恒等式,推广了王永元等关于条件数列二次二项、二次三项乘积和的恒等式.在此基础上讨论了通项是条件数列求和的若干正项级数的敛散性,而这些级数的敛散性用其它方法难以证明.
통과약간초등함수적멱급수전개식급기변형,급출료용기타방법난이증명적조건수렬화적대수항등식,병급출료증명,기중이차s항수렬화적항등식,추엄료왕영원등관우조건수렬이차이항、이차삼항승적화적항등식.재차기출상토론료통항시조건수렬구화적약간정항급수적렴산성,이저사급수적렴산성용기타방법난이증명.
In this paper, some algebra identities on conditional sequences ,which are not easily proved by other methods , have been given and proved by the expansion formulas and their deformations , and the identities on quadratics -nomial conditional sequences generalize the results on quadratic binomial and trinomial conditional sequences given by Wang Yongyuan .Then the convergence of some positive series have been proved , which are not easily proved by other methods .