Mathematics Question from JEE Main 2023 · 6 April, Shift 1

Let $a_1$, $a_2$, $a_3$, ..., $a_n$ be $n$ positive consecutive terms of an arithmetic progression. If $d > 0$ is its common difference, then $\displaystyle\lim_{n\to\infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_1}+\sqrt{a_2}} + \frac{1}{\sqrt{a_2}+\sqrt{a_3}}+ \cdots + \frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right)$ is: