摘 要数列敛散性判定及其极限求解是微积分的基本问题，是学习微积分后续内容的基础，因此对数列做深入的研究与理解，有助于深刻掌握微积分的知识体系。本文主要借助 MATLAB 从数列图形的变化的角度进一步理解数列，在简单介绍了高等数学课程中常见的数列敛散性判定方法及其极限求法之后，着重从数列极限的证明、数列的敛散性判定、有递推关系的数列三个层次通过例子探讨了 MATLAB 的应用，给出了相应例子的 MATLAB 编程并绘制出相应数列的图形，从几何直接观察中对相应的例子提出一定的见解。 关键词：数列；敛散性；极限；MATLABAbstractIt is the basic problem of calculus to determine the convergence and divergence of sequence and to solve its limit, which is the basis of learning the follow-up content of calculus. Therefore, a thorough study and understanding of sequence is helpful to master the knowledge system of calculus. This paper mainly uses MATLAB to further understand the sequence from the point of view of the change of the sequence graph. After a brief introduction to the common determination method of the convergence and divergence of the sequence and its limit solution in the higher mathematics course, it mainly discusses the application of MATLAB from three levels: the proof of the limit of the sequence, the determination of the convergence and divergence of the sequence, and the sequence with recurrence relation. The corresponding MATLAB example is given and the graph of the corresponding sequence is also drawn. Giving some opinions on the corresponding examples from the direct observation of geometry. Key words: sequence; convergence and divergence; limit; MATLAB目 录1 引 言.........................................................12 数列的敛散性判定及数列的极限求法的简介...........................23 MATLAB 在数列中的应用............................................33.1 MATLAB 在证明数列极限中的应用..................
