A) \[3\log 3-2\]
B) \[\frac{18}{{{e}^{4}}}\]
C) \[\frac{27}{{{e}^{2}}}\]
D) \[\frac{9}{{{e}^{2}}}\]
Correct Answer: C
Solution :
\[{{e}^{\underset{n\to \infty }{\mathop{\lim }}\,\frac{1}{n}\sum\limits_{r=1}^{2n}{\ell n}\left( 1+\frac{r}{n} \right)}}=\int\limits_{{{e}^{0}}}^{2}{\ln (1+x)dx}\] \[\Rightarrow \]\[{{e}^{((x+1))\{\ell n(x+1)-1\}_{0}^{2}}}={{e}^{3\ell n3-2}}=\frac{27}{{{e}^{2}}}\]
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