求极限与递代法

Finding Limit and Successive Substitution

求某类数列的极限，用极限的运算法则或洛比达法则都不行，首先必须肯定这个极限存在，然后才能求出这个极限。这类极限的求出是相当复杂的。在本文中，证明了递代法的一个定理，并给出了它的两个应用，从而，在解决上述类型的极限问题时，简捷地获取了结果。

Finding limit of a kind of sequences of number,sometimes to apply operational rule of limit or L’hospital rule cannot already succeed,must first affirm existence of the limit,and then can only find the limit.Finding of this kind of limit is quite complicated.In this paper,is proved a theorem of successive substitution,and are gived its two applications,thus are succinctly obtained the results as solving above-mentional limit problems.