关于极限lim■(1+(1/n))~n的一个推广

ON THE EXTENSION OF lim■(1+1/n)~n

本文证明了数列{(1+(1/n)+a)~n}收敛于e的充要条件,从而提供了对此类极限的一个简易的判别方法,可供教学参考。

In this paper we have shown that infinite sequence {(1+1/n+a)~n} converges to e if and only if lim na=0, As a result, a simple convergence criterion is provided for this type of limit.