Let $a_1, a_2, a_3 \ldots a_n$ be $n$ positive consecutive terms of an arithmetic progression. If $d0$ 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 \frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right) $ [JEE Main 2023, 6 Apr (Shift 1)]

Question

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 \frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right) $ [JEE Main 2023, 6 Apr (Shift 1)]

YESPYQ · Accepted Answer

Options are free to see. Unlock the correct answer and full explanation with PYQ Pass.

Let \(a_1, a_2, a_3 \ldots a_n\) be \(n\) positive consecutive terms of an arithmetic progression. If \(d>0\) is its …

Practice more JEE Maths PYQs

Let \(a_1, a_2, a_3 \ldots a_n\) be \(n\) positive consecutive terms of an arithmetic progression. If \(d&gt;0\) is its …

Practice more JEE Maths PYQs

Let \(a_1, a_2, a_3 \ldots a_n\) be \(n\) positive consecutive terms of an arithmetic progression. If \(d>0\) is its …