An algebra problem by Aira Thalca

Algebra Level 3

Consider the recurrence relation \(f(1) + f(2) + \cdots + f(n) = n^2 \times f(n) \) for \(n=2, 3,\ldots \) with \(f(1) = 2016\).

If the value of \(f(2016) \) can be expressed as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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