The alternating series equals

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

Problem

The alternating series

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

equals

\ln 2

. What is the least integer

N

such that the absolute error in approximating

\ln 2

by the

N

-term partial sum is less than

0.001

? (a)

999

(b)

1000

(c)

1001

(d)

500