x/(1+x)=(x+1-1)/(x+1)
=1-1/(x+1)
令1/a=-1/(1+x)
则a趋于无穷
x=-a-1
所以原式=lim(1+1/x)^(-a-1)
=lim[*1+1/x)^a]^(-1)*1/(1+1/a)
=e^-1*1
=1/e