JEE Mains · Maths · STD 12 - 7.2 definite integral
\(\mathop {\lim }\limits_{n \to \infty } {\left( {\frac{{\left( {n + 1} \right)\left( {n + 2} \right) \ldots .\;3n}}{{{n^{2n}}}}} \right)^{\frac{1}{n}}} = \)
- A \(\frac{9}{{{e^2}}}\)
- B \(3\log 3 - 2\)
- C \(\;\frac{{18}}{{{e^4}}}\)
- D \(\;\frac{{27}}{{{e^2}}}\)
Answer & Solution
Correct Answer
(D) \(\;\frac{{27}}{{{e^2}}}\)
Step-by-step Solution
Detailed explanation
\({e^{\mathop {\lim }\limits_{n \to \infty } \frac{1}{n}\sum\limits_{r = 1}^{2n} {\ell n\left( {1 + \frac{r}{n}} \right)} }} = {e^{\int\limits_0^2 {\ln \left( {1 + x} \right)dx} }}\)…
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