数列极限迫敛性定理的推广(英文)

The Generalization on Squeeze Theorem of Limit of Sequence

极限论是微积分中基础和重要的概念.数列极限的迫敛性定理既能判断数列的收敛性,也给出其极限值。通过对数列极限迫敛性定理的条件加以改进,得到了它的推论,并用一个例子说明了该推论的应用。

The concept of the limit is a very fundamental and important idea in Calculus. The squeeze theorem gives an approach to prove the convergence of a given sequence and find its limit at the same time. With the improving the conditions, two corollaries of the squeeze theorem are shown in this paper. As an illustration, an example is given which involves the property of series.