Deciphering an equation

Algebra Level 3

Assume we have series $$f(1), f(2), \ldots , f(n)$$, where $$f(i)$$ is a function defined for natural numbers. We know that this is true

$$\sum _{ k=1 }^{ n }{ f(k) } =f(n)(n+1)-n$$

Find the function $$f(n)$$

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