## Calculus (3rd Edition)

The series $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{ n^{1/3}}$ converges conditionally.
We have the absolute series $$\sum_{n=1}^{\infty} |\frac{(-1)^{n-1}}{ n^{1/3}}|=\sum_{n=0}^{\infty} \frac{1}{n^{1/3}}$$ which is a divergent p-series as $p=1/3\lt 1$. The series $\frac{1}{ n^{1/3}}$ is positive, decreasing and tending toward zero. Thus, the original series converges by the Alternative Series Test. Therefore, overall the series converges conditionally.