# Thread: Absolute convergence & root/ratio tests

1. ## Absolute convergence & root/ratio tests

Absolutely convergent, conditionally convergent or divergent?

$\sum^{\infty}_{n=1} \frac{(-1)^{n+1}}{\sqrt[3]{n}}$

I thought that this would be divergent via the p-series test with p<1 but that isn't correct. What do I do with this?

2. $|a_n|=\frac1{\sqrt[3]n}$ so it does not coverge absolutely.

Now, use Leibniz test if the original converges, if so, thus the series converges conditionally.