中文摘要：

压缩映像是刻画度量空间与度量空间之间的一种特殊的函数关系。在函数满足一定的条件下,根据压缩映像原理可以求出函数唯一的不动点。基于该性质对一类具有递推形式的数列的极限问题进行研究,用具体实例说明压缩映像原理在求解数列极限问题中非常有效。

英文摘要：

Contractive mapping depicts a special kind of function relationship between two metric spaces.According to contraction mapping theory,the only fixed point can be derived when the function meets some special conditions.Based on this property of contradiction mapping theory,we will investigate the limitation problem of a class of series in a recursive manner.Some specific examples are carried out to demonstrate the effectiveness of contraction mapping theory in solving the limitations of series.