Answer
Series Converges by Theorem 9.14
Work Step by Step
$\Sigma^{\infty} _ {n+1} (-1)^n \frac{1}{\ln(n+1)}$
Apply Alternating Series Test
i.)$ \lim\limits_{n \to \infty} \frac{1}{\ln(n+1)}=0$
ii.) $a_{n+1} = \frac{1}{\ln(n+2)} \leq \frac{1}{\ln(n+1)} =a_n$
Series Converges by Theorem 9.14
