The alternating series converges to

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

Problem

The alternating series

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

converges to

S=\dfrac{\pi^{2}}{12}

. Determine the smallest integer

N

such that

|S-S_N|<0.0005

. (a)

32

(b)

44

(c)

45

(d)

43