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 lim_n → ∞ √(d/n)(1/(√…

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