lim(n→∞)[(n+3)/(n+1)]^n=lim(n→∞){[1+2/(n+1)]^(n+1)}/[1+2/(n+1)]=lim(n→∞){[1+2/(n+1)]^(n+1)/2}^2/lim(n→∞)[1+2/(n+1)]={lim[(n+1)/2→∞][1+2/(n+1)]^(n+1)/2}^2/(1+0)=e^2/1=e^2。
