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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 $\lim _{n \rightarrow \infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+\ldots \ldots .+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right)$

• ✓
  $1$
• B
  $\sqrt{ d }$
• C
  $\frac{1}{\sqrt{ d }}$
• D
  $0$