利用单调有界原理证明下列数列的极限存在，并求出极限值.1. x_0 = 1, x_1 = 1 + (x_0)/(1 + x_0), x_(n+1) = 1 + (x_n)/(1 + x_n) (n = 1, 2, ...);2. 设 a > 0, x_1 > 0, x_(n+1) = (1)/(2)(x_n + (a)/(x_n)) (n = 1, 2, ...);3. 0 < x_n < 1, 且 x_(n+1)(1 - x_n) geq (1)/(4) (n = 1, 2, ...).

利用单调有界原理证明下列数列的极限存在，并求出极限值. 1. $x_0 = 1$, $x_1 = 1 + \frac{x_0}{1 + x_0}$, $x_{n+1} = 1 + \frac{x_n}{1 + x_n}$ ($n = 1, 2, \cdots$); 2. 设 $a > 0$, $x_1 > 0$, $x_{n+1} = \frac{1}{2}\left(x_n + \frac{a}{x_n}\right)$ ($n = 1, 2, \cdots$); 3. $0 < x_n < 1$, 且 $x_{n+1}(1 - x_n) \geq \frac{1}{4}$ ($n = 1, 2, \cdots$).