正项级数比值判别法的推广

Application of Comparison Discriminant of Positive Series

利用函数性质和函数与数列的关系,给出并证明了正项级数达朗贝尔比值判别法和近年来提出的双比值判别法的推广,得到了一般性结论.它们使众多定理成为其特殊情况.文中提出的方法,不但使用简便,具有广泛的适用性,而且更为精细,解决了当limn→∞an+1an=1时,达朗贝尔比值判别法失效情况下敛散性的判定,为正项级数敛散性判定提供了更有力的工具.

Based on function and the relationship between function and progression, comparison discriminant of positive series in accordance with A＇lembert＇s principle is given and confirmed, its conclusion is made, exceptions are found in many theorems. Its simplicity and accuracy make it possible to be widely used, serving for the judgment of its convergence and divergence.