一楼灌水,二楼不严格.
lim x[ln(x+1)-lnx]
x→∞
=lim x[ln(x+1)/x]
x→∞
=lim x[ln(1+1/x)]
x→∞
=lim [ln(1+1/x)^x]
x→∞
=lne
=1