We have:
$$\frac{(-1)^{0}}{0!} = \frac{1}{1} = 1$$
$$\frac{(-1)^{1}}{1!} = \frac{-1}{1} = -1$$
$$\frac{(-1)^{2}}{2!} = \frac{1}{2} = 0.5$$
$$\frac{(-1)^{3}}{3!} = \frac{-1}{6} \approx -0.1667$$
$$\frac{(-1)^{4}}{4!} = \frac{1}{24} \approx 0.0417$$
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