求极限 lim(n+1/n+2)^n.n趋向无穷
问题描述：
求极限 lim(n+1/n+2)^n.n趋向无穷
答
lim((n+1)/(n+2))^n
=lim((1-1/(n+2))^(n+2)^(-1/(n+2))*n
底数(1-1/(n+2))^(-(n+2))趋于e
指数(-1/(n+2))*n趋于-1
lim((n+1)/(n+2))^n
=1/e
答
是不是 求lim[(n+1)/(n+2)]^n?如果是的话极限是e，用高数中的两个重要极限之一就可以了
答
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