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Q.(i) Evaluate (with the help of definite integral)
$\underset{n\to \infty }{\lim }\left[{\left(1+\frac{1^2}{n^2}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$n^2$}\right.} {\left(1+\frac{2^2}{n^2}\right)}^{\raisebox{1ex}{$4$}\!\left/ \!\raisebox{-1ex}{$n^2$}\right.} {\left(1+\frac{3^2}{n^2}\right)}^{\raisebox{1ex}{$6$}\!\left/ \!\raisebox{-1ex}{$n^2$}\right.}....... {\left(1+\frac{n^2}{n^2}\right)}^{\raisebox{1ex}{$2n$}\!\left/ \!\raisebox{-1ex}{$n^2$}\right.}\right]$
(e) (i) Ans : $\frac{4}{e}$