$e^{-x}=1-x+\frac{x^2}{2}-\frac{x^3}{3!}+$cdots

and

$e^{-x}=\frac{1}{e^x}=\frac{1}{1+x+\frac{x^2}{2}+\frac{x^3}{3!}+\text{c}\text{d}\text{o}\text{t}\text{s}}$

and compare with the true value of $6\mathrm{.}737947{10}^{-3}.$ Use $20$ terms to evaluate each series and compute true and approximate relative errors as terms are added.

You will:

Create a Python file called A$1\_$task$3.$py that: