Consider the series

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

Problem

Consider the series

\displaystyle\sum_{n=1}^{\infty}(-1)^{n-1}\dfrac{1}{3n}

. Determine the smallest integer

N

such that the absolute error

|S_N-S|

between the

N

th partial sum

S_N

and the exact sum

S

of the series is less than

0.01