Just observe it

Algebra Level 5

f(1)+f(2)+f(3)++f(n)=n2f(n) \large f(1) + f(2)+ f(3) + \ldots + f(n) = n^2 f(n)

Consider a function f(x)f(x) satisfying the equation above for n1n \geq 1 with f(1)=2005f(1) = 2005.

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

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