幂级数在条件数列中的应用  

The appilications of power series on the conditional sequences

作　　者：陈引兰[1] 余立婷[1] 

机构地区：[1]湖北师范学院数学与统计学院,湖北黄石435002

出　　处：《湖北师范学院学报（自然科学版）》2013年第2期85-90,共6页Journal of Hubei Normal University(Natural Science)

基　　金：湖北师范学院科研项目(NO:2006D12)

摘　　要：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。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.

关 键 词：条件数列 幂级数 敛散性 

分 类 号：O173.1[理学—数学]