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Calculus Level pending

On the interval \(-\pi \leq x \leq \pi\), \(x^2\) can be expressed as an infinite sum of cosines, in the following form:

\[\large x^2= \dfrac{\pi^a}{b} +4 \sum_{n=1}^{\infty} (-1)^n \dfrac{\cos nx}{n^c}\]

Find \(a+b+c\)

Clarification: \(a, b, c\) are constants.

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