# Interacting Integ

Calculus Level 5

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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