lim(n→∞) ln(n+2)^n=lim(n→∞)(n/n+1) *ln[(n+1)+1]^(1/(n+1))
=lim(n→∞)1/(1+1/n) *ln[(n+1)+1]^(1/(n+1))
=lim(n→∞)1/(1+1/n)*lne
=1