$(1$ point$)$

Use the alternating series estimate for the error when using series

$f(x)=1-2x+\frac{2^2}{2!}{x}^2-\frac{2^3}{3!}{x}^3+$cdots

to approximate $f(1)$ with a $4$th$-$degree Taylor polynomial.

$|f(1)-P_4(1)|$