Question 118
Let $M$ be a positive integer, and $A = \{1, 2, \dots, M+1\}$. Show that if $f$ is a bijection from $A$ to $A$ then
$$
\sum_{n=1}^{M} \frac{1}{f(n) + f(n+1)} \gt \frac{M}{M+3}.
$$
$$
\sum_{n=1}^{M} \frac{1}{f(n) + f(n+1)} \gt \frac{M}{M+3}.
$$