Taylor polynomial problem

Hi -

I'm given a problem where I must find the "minimum order of the Taylor polynomial required to approximate the quantity with an absolute error no greater than 10^-3", where the given quantity is e^-0.5

I've calculated the remainder to be R(-0.5)=[0.5^(n+1)]/(n+1)!, yet I do not know how to solve the inequality 10^-3>[0.5^(n+1)]/(n+1)!

I know the answer is supposed to be n=4, but I have no clue how to solve for n. Any help???

Thanks!!

Re: Taylor polynomial problem

Re: Taylor polynomial problem