Division Throughout

Calculus Level 4

\[ \lim_{n \to \infty} \sum_{r=1}^n \dfrac{ \sqrt{n}}{ \sqrt{r} \times(3\sqrt{r} + 4\sqrt{n})^{2}} \]

If the series above can be stated in terms of \(\frac a b\) where \(a,b\) are coprime positive integers, find \(a+b\).

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