"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 \(a+b\).
by
Samir Khan