VMO 1998 Problem 1

Define the sequence $x_1$, $x_2$, $x_3$, ... by $x_1$ = a ≥ 1, $x_{n+1}$ = 1 + ln($x_n$($x_n^2$+3)/(1 + $3x_n^2$) ). Show that the sequence converges and find the limit.