Just observe it

Algebra Level 5

\[ \large f(1) + f(2)+ f(3) + \ldots + f(n) = n^2 f(n) \]

Consider a function \(f(x)\) satisfying the equation above for \(n \geq 1 \) with \(f(1) = 2005\).

Find the sum of digits of \( \dfrac{1}{f(2004)}.\)

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