Consider the alternating series

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

Problem

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

. What is the smallest integer

N

such that the partial sum

S_N

is guaranteed to approximate the series within

0.001

? (a)

N=7

(b)

N=8

(c)

N=9

(d)

N=6