# 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 $$\dfrac{1}{f(2004)}.$$

×