>>973

lim(2n/(2n+1))^n (n→∞)
=lim(1-1/2n+1)^((2n+1)*n/(2n+1)) (n→∞)
=lim((1-1/2n+1)^(2n+1))^(n/(2n+1)) (n→∞)
=lim((1-1/2n+1)^(2n+1))^(1/(2+1/n)) (n→∞)
=e^(1/2)