limx→∞[(x+1)/(x+2)]^x

问题描述:

limx→∞[(x+1)/(x+2)]^x

(x+1)/(x+2)=1-1/(x+2)
所以令1/a=-1/(x+2)
x=-a-2
原式=ima→∞[(1+1/a)^(-a-2)]
=ima→∞[1/(1+1/a)^a]÷(1+1/a)²
=1/e