The series is approximated by

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

Problem

The series

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

is approximated by

S_{4}

. Determine whether

S_{4}

is guaranteed to approximate

S

with absolute error no greater than

\dfrac{1}{800}

. Support your conclusion with a numerical bound.