对Kummer判别法的讨论

Discussion on the Kummer Test

比式判别法和根式判别法是对正项级数收敛性进行判别的两种广用的方法．但如果正项级数的通项收敛于零的速度较某一几何级数的通项收敛于零的速度慢，这两种方法则无用．先讨论一个判别范围更广的Kummer判别法，并将传统的几种方法作为此判别法的一种特例给出．

The ratio test and the root test are two widely used convergence tests for positive series. However, if the underlying sequence of positive series converges slower than that of any geometric series, these two tests do not work. In this paper the Kummer test with a wider test range was discussed, with some traditional tests as its special cases.