# 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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