Answer
Diverges
Work Step by Step
Consider, $a_n=\lim\limits_{n \to \infty} \dfrac{3^{n-1}+1}{3^n}$
or, $\lim\limits_{n \to \infty} \dfrac{3^{n-1}+1}{3^n}=\lim\limits_{n \to \infty} \dfrac{3^{n-1}}{3^n}+\lim\limits_{n \to \infty} \dfrac{1}{3^n}=\frac{1}{3}+0\ne 0$
Hence, the series diverges.