Answer
Limit Does Not Exist(divergent)
Work Step by Step
Let $\lim\limits_{n \to \infty} a_n= \lim\limits_{n \to \infty}
n\pi \cos (n \pi)$
Since, $\cos (n \pi)=\pm 1$; value depends on the value of $n$
This implies that, $\lim\limits_{n \to \infty} n\pi \cos (n \pi)= n\pi (-1)^n$
Hence, the Limit Does Not Exist(divergent)
