Could someone help me out with this problem?

Use the definition of a maclaurin series to find the maclaurin series of f(x) = e^2x (got (2x)^n / n! (from n=0 to infinity). How many terms of the series are required so that the error of the approximation is at most 0.01 for all x in the interval [-2, 2] (using taylor's inequality).

Please show your work, thanks