2025 VIMC keystage3-IWYMIC individual Question 13

Let $n$ be any integer where $n\ge2$. Now, consider all the fractions in the form $\frac1{pq}$, where $\gcd(p,q)=1$, $0\lt p\lt q\le n$ and $p+q>n$. Prove that the sum of all such fractions is $\frac12$.