## Stolz定理及其应用+文献综述

Stolz Theorem and Its Applications
Abstract: Stolz Theorem is a effective method to handle the limit of a sequence in mathematical analysis, we can make it applied to the set of real numbers function form, so that the Stolz theorem and L'Hospital law could closely together, it expand the application of Stolz theorem in the limit of function. In this paper, first give the discrete Stolz Theorem, its geometric significance and several frequently used inference, and then the theorem is extended to the set of real numbers, we gain the Stolz Theorem of continuous type.At last ,we explored the application that how to use the Stolz Theorem to prove the other relative theorem, to solve the limit of a sequence, and progressive application aspect.
Key words: Stolz Theorem; Sequence; Extension; Limit

1.Stolz定理.3
1.1 ( ) 型Stolz定理3
1.2 ( ) 型Stolz定理.6
2.Stolz定理的推广.6
2.1 Stolz定理推广到实数集函数连续形式 7
2.2 Stolz定理推广到无穷级数求和形式12
3.Stolz定理的应用14
3.1 Stolz定理在证明其他相关定理方面的应用 14
3.2 Stolz定理在求极限方面的应用.17
3.3 Stolz定理在研究数列渐进性方面的应用 .19

Stolz定理及其应用引言
数列极限理论在数学分析中占有重要地位,数列极限的求法方法多样.对满足Stolz定理条件的比式极限,运用定理极大地简化了求解的难度,本文将离散的Stolz定理推广到实数集,使其与L'Hospital法则紧密联系,近而对Stolz定理的应用方面加以探究.近年来,一些国内外的专家学者也对Stolz定理及其应用的问题进行了深入的探究,并取得了一些丰富的学术成果,主要是Stolz定理的推广和其在极限方面的应用,从而使得对Stolz定理的认识又上升到了一个新的水平.然而对于Stolz定理的应用方面,有待进一步的深入研究,使之达到更高的理论研究水平,并促进其在实践方面的应用.

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