KG-MO 2009 Problem 9

For any positive $a_1 ,a_2 ,...,a_n$ prove that $\frac {{a_1 }} {{a_2 + a_3 }} + \frac {{a_2 }} {{a_3 + a_4 }} + ... + \frac {{a_n }} {{a_1 + a_2 }} > \frac {n} {4}$ holds.