数列极限计算的若干方法

摘要

本文是探讨不同种类数列极限的求解方法，分别从简单数列和一些较为复杂的数列两方面去探讨求解数列极限，在简单数列中，我们主要利用定义，极限的四则法则，迫敛性等方法，去求解不同类型的简单数列极限.在求解复杂的数列中，将复杂数列具体的分成了三大类：递推数列，n项和数列，一些用特殊的通项表示的数列.根据不同的数列分别用不同的方法去求解，例如：单调有界定理，级数有关性质，定积分性质等.在本文中针对不同类型的数列用具体的方法与相关例子相结合去求探讨求解数列的极限，通过本文的探讨能让我们熟练的求解出针对不同类型的数列极限.

关键词：数列；极限；有界；级数；积分

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Studies on Several Methods of Sequence Limit

ABSTRACT

This article is to explore the different kinds of sequence limit method, mainly from two aspects of simple sequence and some of the more complex the sequence to solving the sequence limit, in the simple sequence, we mainly use of definition, the four principles of limit, forced convergence and so on, to solve different types of simple sequence limit. In solving complex sequence, the complex sequence of concrete is divided into three categories, mainly divided into recursive sequence, and sequence, some use special general representation of the sequence. Then according to the different series with different methods respectively to solve, such as monotonous have defined, series related to nature, nature of definite integral, and so on. In this paper by concrete method combined with relevant examples to solve different types of sequence limit.

Keywords：The Sequence；Limit；Bounded；Series；Integral

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目录

引言 ................................................................................................................................................1 一 基础知识 ..................................................................................................................................1 （一） 、数列极限的思想 ......................................................................................................1 （二） 、数列极限的有关定理. .............................................................................................1 二 简单数列极限求法 ..............................................................................................................2 （一）、利用极限定义和性质求解数列极限 ........................................................................2 （二）、利用数列变形化简求解数列极限 ............................................................................4 （三）、利用公式lim(1?)n?e求数列极限 .....................................................................6

n??1n（四）、利用归结原理求数列极限 ........................................................................................6 三 复杂数列极限求法 ..............................................................................................................7 （一）、利用三大定理求数列极限. .......................................................................................7 （二）、利用级数性质去求数列极限 ..................................................................................10 （三）、利用定积分有关性质求数列极限. .........................................................................12 四 结论 ......................................................................................................................................16 参考文献 ......................................................................................................................................17 致谢 ..............................................................................................................................................19

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