Consider the series

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

Consider the series

\displaystyle e^{-1}=\sum_{k=0}^{\infty}\dfrac{(-1)^k}{k!}

. What is the smallest integer

n

such that using the first

n

+1 terms (from

k=0

k=n

) guarantees an approximation of

e^{-1}

whose error does not exceed

5\times10^{-5}