# root or ratio

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. ### root/ratio tests

i need an example of a series of positive real numbers which converges by the root test, but where the ratio test is not useful at all it has to do done using the strict senses of root and ratio tests which involve only upper limits (limsup), not limits in the strong sense i would be...