发散级数的“求和”问题

The Sum Problem of the Divergent Series

文章主要是对满足某些条件的发散级数给出两种不同的求“和”定义,即算术平均求和与Abel求和,它与通常数学分析中Cauchy意义下所定义的求和是有区别的。讨论在这种广义求“和”定义下级数收敛的必要条件以及它们之间的关系,得出算术平均求和要强于Abel求和结论。

This text is about the divergent series that is satisfied with some conditions to give two different definition of sum, that is, the Arithmetic Sum and the Abel Sum. They are different from the definition of sum, which Cauchy gives. Discuss the necessary condition of the Convergence Series in these two definitions and the relationship between them .As a result, the arithmetic sum is stronger than the Abel sum.