For the following alternating series,
$\displaystyle \sum_{n=1}^\infty a_n = 1 - \frac{(0.5)^2}{2!} + \frac{(0.5)^4}{4!} - \frac{(0.5)^6}{6!} + \frac{(0.5)^8}{8!} - ...$
how many terms do you have to go for your approximation (your partial sum) to be within 0.0000001 from the convergent value of that series?