关于重要极限limn→∞(1+n^(-1))~n=e的2个证明

Two proof about the important limit limn→∞(1+n^(-1))~n=e

在高等数学中,limn→∞(1+1/n)~n=e是一个非常重要的极限,关于它存在性的证明以及应用有很多.给出了limn→∞(1+1/n)~n=e的一个简洁证明,作为扩展给出了e为无理数的一个证明.

In the studies of advanced mathematics, limn→∞（1＋n^-1）^n=e is a very important limit, there is much research work on its existence and application. The limit limn→∞（1＋n^-1）^n=e is proved concisely and as an extension, the proof about e being an irrational number is also given.