the twisting and turning infinite sum of...

$\displaystyle \frac{2}{5} - \frac{3}{10} + \frac{4}{15} - \frac{5}{20} + \frac{6}{25} - \frac{7}{30} + ... $

so I think the series looks like:

$\displaystyle \sum_{n=1}^{\infty}{\frac{(-1)^{n-1}*(n+1)}{5n}}$

looks a little bit geometric, the problem is to show that it either converges or diverges, we have the powerful limit comparison test at our disposal but I am not sure what to compare it to, or if there is an alternate path to solution,

I have tried the integral, basic comparison and nth term tests...

any help kindly appriciated!

thank you!!