Answer
Converges by Theorem 9.14
Work Step by Step
$\Sigma^{\infty} _{n=1} cos(n \pi) \frac{1}{n}$
Apply Alternating Series Test
i.) $\lim\limits_{n \to \infty} \frac{1}{n}=0$
ii.) $a_{n+1} = \frac{1}{n+1} \leq \frac{1}{n} = a_n$
Series Converges by Theorem 9.14
