Limits Continuity And Differentiability

Let \(a_{1}, a_{2}, a_{3}, \ldots, a_{\mathrm{n}}\) be \(\mathrm{n}\) positive consecutive terms of an arithmetic progression. If \(\mathrm{d} > 0\) is its common difference, then

\(\lim_\limits{n \rightarrow \infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots \ldots \ldots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}\right)\) is