If the sequence \(a_n = e^{-n} + (-1)^n cos^3(\frac{19}{e^3})^n+ (-1)^n (sin(\frac{1}{n^2}+ \frac{(-1)^n \pi }{2}))\) then choose the correct option?
1
largest limit point of the sequence is greater than e
2
the sequence is converges in (-1, e)
3
the sequence is not converges in (-1, e)
4
\(lim_{n \to \infty } \ inf \ a_n = 1\)