# Polylog of primitive root of unity

Calculus Level 5

$\large \sum_{\omega\in W} \text{Li}_2(\omega x) = \sum_{n=1}^{2015} a_n \text{Li}_2(x^n)$ The equation above holds true where $$W$$ is the set of the $$2015^\text{th}$$ primitive roots of unity.

If the value of $$\displaystyle \sum_{n=1}^{2015} a_n$$ can be expressed as $$-\dfrac AB$$, where $$A$$ and $$B$$ are coprime positive integers, find $$A+B$$.

Notation:
$${ \text{Li} }_{ n }(a)$$ denotes the polylogarithm function, $${ \text{Li} }_{ n }(a)=\displaystyle\sum _{ k=1 }^{ \infty }{ \frac { { a }^{ k } }{ { k }^{ n } } }.$$

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