JEE Main 202127 Aug, Morning shiftMathematicsMediumIntegral Calculus369× since 2002If Un=(1+1n2)(1+22n2)2.....(1+n2n2)n{U_n} = \left( {1 + {1 \over {{n^2}}}} \right)\left( {1 + {{{2^2}} \over {{n^2}}}} \right)^2.....\left( {1 + {{{n^2}} \over {{n^2}}}} \right)^nUn=(1+n21)(1+n222)2.....(1+n2n2)n, then limn→∞(Un)−4n2\mathop {\lim }\limits_{n \to \infty } {({U_n})^{{{ - 4} \over {{n^2}}}}}n→∞lim(Un)n2−4 is equal to :AOption A. e216{{{e^2}} \over {16}}16e2BOption B. 4e{4 \over e}e4COption C. 16e2{{16} \over {{e^2}}}e216DOption D. 4e2{4 \over {{e^2}}}e24CheckSkip · show solution
