# A Fractional Periodicity

Algebra Level 3

$\large f(x) = \lfloor x\rfloor + \lfloor 2x\rfloor + \lfloor 3x\rfloor + \cdots + \lfloor nx\rfloor - \dfrac{n(n+1)}2 x$

Find the fundamental period of the function above.

Notation: $$\lfloor \cdot \rfloor$$ denotes the floor function.

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