Answer
The Ratio Test is inconclusive.
Work Step by Step
Given
$$\sum_{n=2}^{\infty} \frac{1}{\ln n}$$
By using the Ratio Test, we get:
\begin{align*}
\rho&=\lim _{n \rightarrow \infty}\left|\frac{a_{n+1}}{a_{n}}\right|\\
&=\lim _{n \rightarrow \infty}\frac{\ln (n+1)}{\ln n} \\
&= \lim _{n \rightarrow \infty} \frac{\frac{1}{n+1}}{\frac{1}{n}}\\
&= \lim _{n \rightarrow \infty}\frac{n}{n+1}\\
&=1
\end{align*}
Thus the Ratio Test is inconclusive.
