数列算术平均序列的收敛性

Convergence of Arithmetic Mean Sequence for a Number Sequence

对一般数列的情况进行了讨论,给出了数列的子列权的概念,得出了关于数列的算术平均序列的一个定理,即存在有限划分的收敛子列的数列,其算数平均序列收敛于其子列极限的线性组合,而系数正是相应子列的权。对其他的一些情况也进行了讨论。

In this paper,the weight of a subsequence for a number sequence is defined,then a theorem,that is,an arithmetic mean sequence for a sequence with finite partition corre spond to convergent subsequence convergence to a li near combination of subsequence limit and the coefficient are the weight of a subsequence,is given.After that,more con clu sions are obtained.