Mathematics

Problem

For the series

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

, let

S_{n}

denote the

n

th partial sum. Three classmates claim that their approximations meet an error tolerance of

0.01

. I. Alex uses

S_{2}

. II. Bailey uses

S_{3}

. III. Casey uses

S_{4}

. Which of the following identifies all classmates whose approximation is guaranteed to meet the stated tolerance? a) Bailey and Casey only b) Casey only c) None of them d) Alex, Bailey, and Casey

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