_ n ( 1 + 1 n^2 ) ( 1 + 2^2 n^2 ) ( 1 + 3^2 n^2 )...... ( 1 + (n … - Vidyadip

MCQ

$\mathop {\lim }\limits_{n \to \infty } {\left\{ {\left( {1 + \frac{1}{{{n^2}}}} \right)\left( {1 + \frac{{{2^2}}}{{{n^2}}}} \right)\left( {1 + \frac{{{3^2}}}{{{n^2}}}} \right)......\left( {1 + \frac{{{{(n - 1)}^2}}}{{{n^2}}}} \right)} \right\}^{1/n}}$ Equals to:-

A
${e^{(4 - \pi )/2}}$
B
${e^{(\pi - 4)/2}}$
✓
$2{e^{(\pi - 4)/2}}$
D
None

✓

Answer

Correct option: C.

$2{e^{(\pi - 4)/2}}$

c

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