判别常数项级数敛散性易犯错误分析研究

Analysis on Easy Wrong Topic of Testing the Convergence and Divergence of Constant Series

学员在判别常数项级数敛散性的过程中经常出错.文中对学员易犯的错误进行了分析总结,其常见的错误类型主要有:利用级数收敛的必要条件来判断级数收敛;颠倒级数收敛与级数的和的逻辑顺序;乱用比较审敛法;误认为比值审敛法是充要条件等等.文中就每种错误给出了相应的例题,对错解进行了分析,最后给出了正确解法.

Most of the students often make mistakes when testing the convergence and divergence of constant series. The errors in the process of problem solving are concluded. The common errors are as follows: using the necessary conditions for convergence of the series,reversing the logical order of the convergence and the sum of series,misusing the comparison test and ration test are erroneously assumed to be necessary and sufficient condition. Furthermore,some corresponding examples are given for each type of error,the wrong and correct solution are analyzed.