证明数列{(1+1/n)~n}极限存在的几种方法

Several Methods of Proving the Limit Existence of Sequence {(1+1/n)~n}

以二项式定理、各类不等式、构造辅助数列、取对数等为基础,再根据单调有界定理给出证明数列{(1+1/n)~n}极限存在的六种方法。

On the basis of binomial theorem, various inequalities, constructing auxiliary sequence,taking logarithm and so on, and then according to monotone bounded theorem, six methods to prove the existence of limit of sequence {（1＋1/n）~n} are given.