Mathematics

Problem

The Maclaurin series for

e^{-x}

\displaystyle \sum_{k=0}^{\infty}\frac{(-1)^{k}x^{k}}{k!}

. When

x=1

, find the least integer

n

for which the

n

-degree Maclaurin polynomial (containing terms up to

x^{n}

) approximates

e^{-1}

with an error smaller than

0.0001