lim(x→∞) (1+5/x)^2x的极限怎么求?

lim(x→∞) (1+5/x)^2x
=lim(x→∞) (1+5/x)^(2*5x/5)
=lim(x→∞) [(1+5/x)^x/5]^10
=e^10那这个怎么变lim(x→∞) ((2x+3)/(2x+1))^(x+1)lim(x→∞) ((2x+3)/(2x+1))^(x+1)=lim(x→∞) ((2x+1+2)/(2x+1))^(x+1)=lim(x→∞) (1+2/(2x+1))^(x+1)=lim(x→∞) (1+1/(x+1/2))^(x+1)=lim(x→∞) (1+1/(x+1/2))^(x+1/2+1/2)=√[lim(x→∞) (1+1/(x+1/2))^(x+1/2)]=√e