关于莱布尼兹判别法条件的讨论

判断交错级数敛散性的莱布尼兹判别法在判断交错级数收敛时很奏效,但人们往往用它来判断级数的发散,即认为判别法的条件不满足时,交错级数就发散,这是错误的,通过两个例子给以说明,同时给出了判断交错级数发散的某些方法.

A Discussion on the Conditions of leibniz Method of Judging

Leibniz method of judging is an effective way in the judgement of the convergence of crisscross progres-sion. However, this method of judging is generally used to judge the divergence of the progression, for it is be-lieved to be wrong to think that inadequate prerequisite conditions for the theorem will give rise to the divergence of the crisscross progression. To support the idea, this thesis will provide two illustrating examples along with some methods with which the divergence of the crisscross progression can be judged.