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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