Chapter 3, Problem 6P

Evaluate $e^{-5}$ using two approaches

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

and

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

and compare with the true value of $6.737947\times {10}^{-3}$. Use 20 terms to evaluate each series and compute true and approximate relative errors as terms are added.