摘要
下述命题是熟知的:假设 {x_n)_(n=1)~∞是一数列且x_n=a 则1/n x_=a,并且我们知道它的逆命题是不真的。本文给出两个定理和两个推论,定理1断言S_n=1/nx_i 收敛于 a 和 b 的某种组合,这里 a 是(x_n)的子列极限,b 亦如此。在定理2中我们给出1/nx_i=0的一个充要条件,两个推论也是有趣的。
the following proposition is well known:Suppose{x_n}_(n=1)~∞ is a numerical sequence and(?)x_n=a,then we have(?)x_1=a.And we know that the con- verse proposition is not true.In this paper,we give two theorems and two corollaries.The- orem 1 concludes that(?)converges to some combination of a and b,where a is a limit of subsequence and so is b.In theorem 2,we give a sufficient and necessary condi- tion for(?)The two corollaries are of interest.
出处
《中国民航学院学报》
1992年第2期54-59,共6页
Journal of Civil Aviation University of China
关键词
收敛性
有界数列
算术平均
convergence
bounded sequence
arithmetical mean
