求极限lim(n+1/n+3)^n

题目

求极限lim(n+1/n+3)^n
如题

答案

lim [(n+1)/(n+3)]^n
=lim [1-2/(n+3)]^n
=lim {[1-2/(n+1)]^[-(n+1)/2]}^[-n×2/(n+1)]
=lim e^[-2n/(n+1)]
=e^lim -2n/(n+1)
=e^lim [-2/(1+1/n)]
=e^(-2)