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The value of
\( \mathrm{P}^{22: 5} \) \( \lim _{n \rightarrow \infty}\left[\left(1+\frac{1}{n^{2}}\right)\left(1+\frac{2^{2}}{n^{2}}\right) \ldots\left(1+\frac{n^{2}}{n^{2}}\right)\right]^{1 / n} \) is

W
(1) \( \frac{e^{\pi / 2}}{2 e^{2}} \)
(2) \( 2 \mathrm{e}^{2} \mathrm{e}^{\pi / 2} \)
(3) \( \frac{2}{e^{2}} e^{\pi / 2} \)
(4) 0
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