## Multivariable Calculus, 7th Edition

$\Sigma^{\infty}_{n=1} \frac{n-1}{3n-1}$ $\lim\limits_{n \to \infty}a_{n} = \lim\limits_{n \to \infty}(\frac{n-1}{3n-1})$ $= \lim\limits_{n \to \infty} (\frac{1-\frac{1}{n}}{3-\frac{1}{n}})$ $= \frac{1}{3} \ne 0$ The given series diverges since $\lim\limits_{n \to \infty}a_{n} \ne 0$. The series $\Sigma^{\infty}_{n=1} a_{n}$ is divergent.