柯西判别法与达朗贝尔判别法的正确应用

Proper Application of Cauchy Test & D'Alembert's Test

在数值级数中 ,对于一般的的变号级数∑∞n =1un,为了判断该级数是条件收敛还是绝对收敛 ,我们常常将其转化为判别正项级数 ∑∞n=1｜un｜与变号级数 ∑∞n =1un 的敛散性而得到 .在正项级数的判别法中 ,最简单又最常用的是柯西判别法与达朗贝尔判别法 ,但是学生在应用这两个判别法时 ,又经常出现错误 .通过对上述两个判别法的证明过程的分析 ,归纳出一些结论和应注意的地方 ,以便今后少出现错误 .

Cauchy Test and D'Alembert's Test are most widely used to judge positive term series  ∑∞n=1|u n| .In practice, students are apt to make errors in applying them. In the paper the demonstration process of the two tests are analyzed and some comments are made on their proper application.