证明lim(1+1/n)~n(from n=-∞ to ∞)存在的新方法

A New Method of Proving the Existence Of lim(1+1/n)~n(from n=-∞ to ∞)

文章利用构造不等式bn +1 -an +1b -a <(n + 1)bn(0≤a <b)推出数列 {(1+ 1n) n}是单调有界数列 ,从而证明了limn→∞(1+ 1n) n

In this paper,the existence of limn→∞(1+1n)\+n is proven by using inequalityb\+ n+1 -a\+ n+1 b-a<(n+1)b\+n(0≤a<b),which induces that the sequence {(1+1n)\+n} is a monotone bounded sequence.