正项级数比较判别法极限形式的探析

Exploration and analysis on the limit form of positive series comparative discriminant method

大部分高等数学教材都是从极限义出发,给出正项级数比较判别法极限形式的证明方法.从函数极限义的一个等价条件出发,利用无穷小的思路,给出正项级数比较判别法极限形式新的证明方法,对原来的理进行完善,同时给出具体实例说明该理的几种特殊情况.这些结论对正项级数敛散性的判有一的理论意义.

Most of the higher mathematics textbooks give the proof of limit form of positive series comparison discriminant method based on the definition of limit.Starting from an equivalent condition of the definition of function limit and using the idea of infinitesimal,gives a new proof method of limit form of positive series comparison discriminant,perfects the original theorem,and gives some concrete examples to illustrate some special cases of the theorem.These conclusions have certain theoretical significance for the determination of convergence and divergence of positive series.