lim(x→∞) (1 - 2/x)^(x + 1)
= lim(x→∞) [1 + (- 2/x)]^[(- x/2) · (- 2/x) · (x + 1)]
= {lim(x→∞) [1 + 1/(- x/2)]^(- x/2)}^[- 2(x + 1)/x],前面部分如同lim(x→∞) (1 + 1/x)^x = e
= e^lim(x→∞) [- 2(x + 1)/x]
= e^lim(x→∞) - 2 · (1 + 1/x)
= e^(- 2 · (1 + 0))
= e^(- 2)
= 1/e²