Absolute Convergence

Simply take the absolute value of the series and apply any other convergence test that may be applicable.

Given $\sum_{n = 0}^{\infty} \frac{(- 1)^{n}}{n^{4}}$

\begin{aligned} \sum_{n = 0}^{\infty} \frac{(- 1)^{n}}{n^{4}} & = \sum_{n = 0}^{\infty} | \frac{(- 1)^{n}}{n^{4}} | \\ = \sum_{n = 0}^{\infty} \frac{1}{n^{4}} \end{aligned}

Converges as it is a $p$ -series with $p > 1$