# Sum up the powered sines

Calculus Level 4

$\large \lim_{n\to \infty} \sum_{r=1}^{n^2} \frac 1r \sin \left(\frac{2017 r^2}{n^2}\right)$

If the value of the limit above is $\dfrac{a \pi}{b}$, where $a$ and $b$ are coprime positive integers, then what is $a + b?$

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