求极限 lim(n+1/n+2)^n.n趋向无穷

题目

求极限 lim(n+1/n+2)^n.n趋向无穷

答案

lim(n→∞)[(n+1)/(n+2)]^n
=lim(n→∞)1/[(n+2)/(n+1)]^n
=lim(n→∞)1/[1+1/(n+1)]^n
=lim(n→∞)[1+1/(n+1)]/[1+1/(n+1)]^(n+1)
=1/e