Consider the alternating series

MATHEMATICS · Single correct · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

\displaystyle \sum_{k=0}^{\infty}(-1)^k\frac{3}{k^2+1}

. What is the minimum integer

N

for which the absolute error of the partial sum

S_N

is at most

0.002

? (a)

39

(b)

37

(c)

38

(d)

40