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Limits Continuity and Differentiability question

2023 · 6 Apr · Shift 1 · Q32

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JEE Main
Mathematics
Limits Continuity and Differentiability
2023 · 6 Apr · Shift 1 · Q32

Limits Continuity and Differentiability question

2023 · 6 Apr · Shift 1 · Q32

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

Let

a_{1}, a_{2}, a_{3}, \ldots, a_{\mathrm{n}}

be

\mathrm{n}

positive consecutive terms of an arithmetic progression. If

\mathrm{d} \gt 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 \ldots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}\right)

is

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

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