Consider the sequence (an)n ≥ 1, where \(a_n=\cos \left((-1)^n \frac{n \pi}{2}+\frac{n \pi}{3}\right)\). Which one of the following statements is true?
1
\(\displaystyle \limsup _{n \rightarrow \infty} a_n=\frac{\sqrt{3}}{2}.\)
2
\(\displaystyle \limsup _{n \rightarrow \infty} a_{2 n}=1\)
3
\(\displaystyle \limsup _{n \rightarrow \infty} a_{2 n}=\frac{1}{2}.\)
4
\(\displaystyle \limsup _{n \rightarrow \infty} a_{3 n}=0\).