数列{n/(n!)～(1/n)}的单调有界性及极限的证明

The proof on the boundedness,monotonicity and limit of number sequence{n/(n!)～(1/n)}

讨论数列{n/(n!)～(1/n)}的单调有界性与极限的方法很多.利用基本极限与比式方法直接证明数列{n/(n!)～(1/n)}是严格单调递增的且以e为极限,而不必借助导数、级数、积分及Stirling公式等工具.

There are many methods of proving monotonicity, boundedness and limit on the number sequence {n/n√n!}By means of elementary method given an immediate proof that the number sequence{n/n√n!}is strictly monotone increasing and its limit is e. The differentiation, series, integration and Stirling formula are not used in the proof.