Let \(I_{n} = \displaystyle \int_{0}^{\pi} \dfrac{\cos n x \; \mathrm dx}{13-12\cos x}\).

Compute the value of \(\displaystyle \lim_{n\to \infty}(I_{0}+I_{1}+\ldots+I_{n}) \)

If your answer comes in form, \(\dfrac{a\pi}{b}\), where \(a\) and \(b\) are coprime positive integers, then find \(a+b\).

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