| 摘要: |
| 在MOOC模式下将无穷小量的阶与无穷级数比较判别法的极限形式结合起来，通过无穷级数通项对应的等价（或同阶）无穷小量、高阶无穷小量和低阶无穷小量来寻找适当的“参照级数”，解决了正项级数比较判别法的碎片化与知识系统性问题，并举例说明该方法在判定无穷级数收敛性方面的的有效性. |
| 关键词: 正项级数 比较判别法 无穷小量 p-级数 收敛 MOOC 知识碎片化 |
| DOI： |
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| Fragmentization of “Reference Series” of Comparing Discriminant Methods for a Positive Term Series |
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WEN Dao jun， XIA Li，CHEN Yi an
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| Abstract: |
| This paper combines the order of infinitesimality with the limiting form of comparing discriminant methods for a positive term series under the model of MOOC. A proper “reference series” is found by equivalent（or same order）infinitesimality with original series, or high order or low order infinitesimality respectively which general term corresponds to. The problem of fragmentization and knowledge systematicness of the comparing discriminant methods for a positive term series is solved. Moreovr, the effectivity of this method is illustrated by some instances in discriminating the convergence of infinite series. |
| Key words: positive term series comparing discriminant methods infinitesimality p series convergence MOOC knowledge fragmentization |
