A calculus problem by Sutirtha Datta

Calculus Level 3

limn1+2++n1nn=ab \large \lim_{n\to\infty} \dfrac{ \sqrt1 + \sqrt2 + \cdots + \sqrt{n-1}}{n \sqrt n} = \frac ab

The equation above holds true for coprime positive integers aa and bb. Find a+ba+b.

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