Kummer判别法的一种推广形式及应用

An Extended Kummer Criterion and Application

基于正项级数通项的比值 a n+p/ a n ≤ b n+p /b n 的分析,得到了 Kummer 判别法的一种推广形式,进一步给出了其极限表示.对推广的 Kummer 判别法中的赋值,分别得到推广的达朗贝尔判别法,推广的拉贝判别法及推广的贝特朗判别法.类似得到高斯判别法的推广形式.最后通过若干例子验证了方法的有效性.

For positive series, by analyzing the ratio relation a n+p/ a n ≤ b n+p/ b n ,a generalized form of Kummer criterion and its limit expression are proposed. By choosing different forms of b n , various generalized criterions are obtained, including Gaussian criterion. Examples are also used to verify the effectiveness of the method.