If \(\lim_{n \to \infty} \left[\left(1 + \frac{1}{n^2}\right)\left(1 + \frac{4}{n^2}\right)\left(1 + \frac{9}{n^2}\right) \dots \left(1 + \frac{n^2}{n^2}\right)\right]^{\frac{1}{n}} = a e^b,\) then a + b =
1
\(\ \pi - 2\)
2
\(\ \pi\)
3
\(\ \pi + 2 \)
4
\(\ \frac{\pi}{2}\)