Division Throughout

Calculus Level 4

limnr=1nnr×(3r+4n)2 \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 ab\frac a b where a,ba,b are coprime positive integers, find a+ba+b.

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