What is the smallest positive integer such that the th partial sum of approximates…

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

What is the smallest positive integer

N

such that the

N

th partial sum of

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

approximates the series’ sum with an absolute error less than

0.001