infinite series 无限级数；无穷级数
收敛与发散Convergence and Divergence
判别Discriminant
正项级数（positive series）
充要条件necessary and sufficient condition
有界性boundness
d'alembert's Discriminant达朗贝尔判别法
Infinite series is the most important reseach tool in mathematical analysis and application, and discriminant of convergence and divergence of infinite series is generally the problem been paid much attention. This paper prepare to study a new discriminant method for discriminant of convergence and divergence of positive series. It is remarkable that this study is significance in both theory and application.
Generally, the convergence and divergence of positive series depends on the boundness of partial adding sequence ，that is to say, the necessary and sufficient condition for convergence of positive series is that partial adding sequence having bound.
But using the boundness of partial adding sequence to discriminate
the convergence and divergence of series in inconvenient. We introduced useful kummer estimation in this paper, which could detrude d'alembert's Discriminant，La Bell's Discriminant，伯尔特昂Discriminant，Gauss Discriminant etc.