"Lebesgue" Sum

Calculus Level 4

$\large\lim_{n\to\infty} \sum_{i=1}^n \frac{i}{n} \left(\sqrt{\frac{i}{n}}-\sqrt{\frac{i-1}{n}}\right)=\frac{a}{b}$

If the above equation is true for coprime positive integers $a$ and $b$ , find $a+b$ .