Question

lim(n+1/n+3)的n+1次方

Answer 1

问题不够完整。现补充为

求解该极限，首先将极限表达式化简成已知的两个重要极限公式的形式，然后求其极限。

求解过程如下：

Answer 2

lim<n→∞> [(n+1)/(n+3)]^(n+1)
= lim<n→∞> [(n+3-2)/(n+3)]^(n+1)
= lim<n→∞> {[1-2/(n+3)]^[-(n+3)/2]}^[-2(n+1)/(n+3)]
= e^lim<n→∞>[-2(n+1)/(n+3)] = e^(-2) = 1/e^2