1、 毕 业 论 文（设 计） 2011 届 数学与应用数学 专业 0 班级 题 目 数列极限的求法及其应用 内 容 提 要 数列极限可用N语言和AN语言进行准确定义，本文主要讲 述数列极限的不同求法，例如：极限定义求法、极限运算法则法、夹 逼准则求法、 单调有界定理求法、 函数极限法、 定积分定义法、 Stoltz 公式法、 几何算术平均收敛公式法、 级数法、收缩法等等.我们还会发 现同一数列极限可用不同方法来求. 最后我们还简要介绍了数列极限在现实生活中的应用， 如几何中 推算圆面积，求方程的数值解，研究市场经营的稳定性及购房按揭贷 款分期偿还问题.通过这些应用使我们对数列极限有一个更系统立体
2、 的了解. 关键词关键词 N定义；夹逼准则；Stoltz 公式；函数极限 On the Solutions and the Applications as to the Sequence Limit Abstract The limit of a sequence can be accurately defined by N language and AN language. This paper mainly describes different solutions to finding sequence limit, for example, definition of sequence
3、 limit method, fundamental operations of sequence limit method, squeezing law method, the monotone convergence theorem method, function limits method, definite integrals definition method, Stoltz formula method, geomeric and arithmetic convergence formula method, series method, contraction method, e
4、tc. Well also find that different methods can be used to solve the same limit. Finally, we also briefly introduce the applications of sequence limit in real life, such as, infering the area of a circle in geometry, finding the numerial solution of equations, studying the stability of the market operation and the amortization problems of purchase mortgage loans. Key Words Ndefinition; Squeezing law; Stoltz formula; Function limits 目 录 第一章第一章 数列极限的概念数列极限的概念 1 1.1 数列极限
