Question 4
(MON 1) IMO5 Let $d$ be the sum of the lengths of all diagonals of a convex polygon of $n$ $(n\gt 3)$ vertices and let $p$ be its perimeter. Prove that
$$\frac{n-3}{2}\lt \frac{d}{p}\lt \frac12\left(\left[\frac n2\right]\left[\frac{n+1}{2}\right]-2\right).$$
$$\frac{n-3}{2}\lt \frac{d}{p}\lt \frac12\left(\left[\frac n2\right]\left[\frac{n+1}{2}\right]-2\right).$$