Use the alternating series estimation theorem to approximate the sum of $\displaystyle (-1)^n/(n!)$ from n=0 to infinity with an error of $\displaystyle .000005$.

I know that after summing a number of terms, the remainder(error) will be less than the first omitted term, so

I've set up the problem like this:

$\displaystyle .000005 < 1/(n+1)!$

Is this right, and if so, what's next?