TH-TMO 2016 Problem 2

Let $M$ be a positive integer, and $A = \{1, 2,... , M + 1\}$ . Show that if $f$ is a bijection from $A$ to $A$ then $\sum_{n=1}^{M} \frac{1}{f(n) + f(n + 1)} > \frac{M}{M + 3}$