I really need someone to walk me through this step by step. I have no idea how to go about this.

Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy?

$\displaystyle \sum^{\infty}_{n=1} \frac{(-1)^{n+1}}{7n^4}$

$\displaystyle (|error|) < .00005$