Answer
Divergent
Work Step by Step
Let $u_n=\lim\limits_{n \to \infty} \dfrac{3^{n-1}+1}{3^n}$
Now, $\lim\limits_{n \to \infty} \dfrac{3^{n-1}+1}{3^n}=\lim\limits_{n \to \infty} (\dfrac{3^{n-1}}{3^n})+\lim\limits_{n \to \infty} (\dfrac{1}{3^n})$
$\implies \dfrac{1}{3}+0=\dfrac{1}{3} \ne 0$
Thus, the given series is a divergent series.