Function and Triangle are Best Friend

Algebra Level 4

A function is defined as \(f(1) = 2017 \) and \(f(1) + f(2) + \cdots + f(n) = n^2 f(n)\) for all \(n > 1\). Find \(f(2017)\).

If you answer can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, compute \(a+b\).