For the following alternating series,
$\displaystyle \sum_{n=1}^\infty a_n = 0.5 - \frac{(0.5)^3}{3!} + \frac{(0.5)^5}{5!} - \frac{(0.5)^7}{7!} + ...$
how many terms do you have to compute in order for your approximation (your partial sum) to be within 0.0000001 from the convergent value of that series?