正项级数收敛判别法的推广

Generalization of Test for Convergence of Positive Terms Series

首先将柯西定理的条件改变为一般形式,进而将正项级数收敛性判别法中的比值判别法和广义比值判别法进行了推广。

In this paper,we improve the condition in sum from k=1 to ∞(2ka2k)Cauchy Theorem into sum from k=1 to ∞(tkatk(t≥2)).Then we popu-larize the generalized ratio test and ratio test in the convergence for positive term series.