Let . What is the least integer such that the absolute error in using the th partial…

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

Problem

Let

S=\displaystyle\sum_{n=1}^{\infty} (-1)^{\,n+1}\dfrac{1}{n^{3}}

. What is the least integer

N

such that the absolute error

|S-S_N|

in using the

N

th partial sum

S_N

is less than

0.0005

? (a)

N=13

(b)

N=12

(c)

N=14

(d)

N=11