幂级数在条件数列中的应用

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。

The appilications of power series on the conditional sequences

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.