Write a Python code to approximate the exponential function with a series form

$e^x=1+x+\frac{x^2}{2}!+\frac{x^3}{3}!+\frac{x^4}{4}!+$dots

Then use the code to determine the solution of the function for $x=0\mathrm{.}1,0\mathrm{.}5,1.,5,$ and $50$ with $8$ significant figures. Explain the difficulties encountered and ways to improve the computed solutions.