Please help, very stuck on this.

-2n Consider the series E n=0 n! 1. Prove that this series converges. 2. Estimate the sum of this alternating series. Do this by finding the first partial sum where the error for the sum is guaranteed to be less than 0.001. Show /Explain how you know this is actually the first partial sum where that happens! (Hint: Alternating series remainder.)