Answer
$\lim_{n\to\infty}\sin(n\pi/2)$ does not exist.
The sequence is divergent.
Work Step by Step
$a_{n}=\sin(n\pi/2)$
$\lim_{n\to\infty}a_{n}=\lim_{n\to\infty}\sin(n\pi/2)=...$
For all values of $n$, the sequence will oscillate between $1$ and $-1$ and does not approach a definite number. Therefore, the limit does not exists and this is a divergent sequence.
