Answer
a) Converges
b) Diverges
Work Step by Step
a) $\lim\limits_{n \to \infty}$$ a_{n}$ =$\lim\limits_{n \to \infty}$ $\frac{2n}{3n+1}$= $\frac{2}{3}$ since the limit of the sequence $ a_{n}$ exists the sequence converges.
b) Since $\lim\limits_{n \to \infty}$$ a_{n}$ =$\frac{2}{3}$ $\ne$ 0 the series$\sum_{n=1}^\infty$$ a_{n}$ is divergent by the Test for Divergence.
