一个极限问题的两种解法

Two Methods for a Limit Problem

针对第13届美国普特南数学竞赛的一道数列极限题,将原本不具有单调性质的数列转化为单调数列,并利用单调有界原理及数学归纳法,得出其极限,此方法可推广用以解决同类的一般性数列求极限.此外,此题也可采用不动点原理,简化计算过程.

For a limit problem in the 13 th William Lowell Putnam Mathematical Competition,we use,respectively,Monotone convergence theorem and mathematical induction to obtain the limit.Fixed point theorem can be also used for this problem.Our method is simple and elegant.