The series converges to

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

Problem

The series

\displaystyle \sum_{k=1}^{\infty}(-1)^{k+1}\frac{\left(\tfrac12\right)^k}{k}

converges to

\ln\!\left(\tfrac32\right)

. What is the smallest value of

N

that guarantees the partial sum

S_N

differs from

\ln\!\left(\tfrac32\right)

by less than

0.0001

? (a)

N=10

(b)

N=9

(c)

N=13

(d)

N=14