Answer
Diverges
Work Step by Step
The sum of a geometric series can be found as:
$S=\dfrac{a}{1-r}$
Thus, we have $\lim\limits_{n \to \infty} s_n=\lim\limits_{n \to \infty} \ln \dfrac{1}{3^n}=-\infty \ne 0$
Now, $s_n \to \infty$ as $n \to -\infty$, so, the given series diverges.
