Consider the series

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

Problem

Consider the series

\displaystyle \sum_{k=1}^{\infty} \dfrac{(-1)^{k+1}}{k^{2}}

. What is the smallest positive integer

n

such that the absolute error when

S_n

is used to approximate the infinite sum is less than

0.0005

? (a)

63

(b)

45

(c)

44

(d)

43