Answer
Divergent
Work Step by Step
Given: $a_{n}=cos(n\pi/2)$
A sequence is said to be converged if and only if $\lim\limits_{n \to \infty}a_{n}$ is a finite constant.
Now,
$\lim\limits_{n \to \infty}a_{n}=\lim\limits_{n \to \infty}cos(n\pi/2)$
In this case, $a_{n}=[0,-1,0,1,0,-1,0,1,...]$
This implies that the sequence has no limit.
Hence, the given sequence is divergent.
