数学试题讲解

查看原题

设数列

{x_{n}}

满足

x_{n + 1} = \sqrt{\frac{π}{2} x_{n} \sin x_{n}}

, 且

0 < x_{1} < \frac{π}{2}

. 求

lim_{n \to \infty} \frac{\sec x_{n} - \tan x_{n}}{\frac{π}{2} - x_{n}}