Determine ascending functions \(\displaystyle f:\mathbb N^{*} \rightarrow \mathbb N^{*}\) with the property that \(\displaystyle \frac{f(1)+f(2)+\cdots +f(n)}{f(1)f(2)+f(2)f(3)+\cdots +f(n)f(n+1)}=\frac{3}{2f(n)+4}\) \(\displaystyle \forall n \in \mathbb N^{*}\).

All the best,

Integrator