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
