VMO 1992 Problem 3

Given a > 0, b > 0, c > 0, define the sequences $a_{}$, $b_n$, $c_n$ by $a_0$ = a, $b_0$ = b, $c_0$ = c, $a_{n+1}$ = $a_n$ + 2/($b_n$ + $c_n$), $b_{n+1}$ = 2/($c_n$ + $a_n$), $c_{n+1}$ = $c_n$ + 2/($a_n$ + $b_n$). Show that $a_n$ tends to infinity.