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