CMO 1977 Problem 6

Let $0 < u < 1$ and define $$u_1 = 1 + u, u_2 = \frac{1}{u_1} + u, \dots, u_{n + 1} = \frac{1}{u_n} + u, n \ge 1.$$ Show that $u_n > 1$ for all values of $n = 1$ , 2, 3, $\dots$ .