For the series

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

Problem

For the series

\displaystyle \sum_{n=0}^{\infty}\dfrac{(-1)^{n}}{2n+1}

, what is the least number of terms that must be summed so that the approximation is guaranteed to be within

0.0005

of the true value? (a)

999

(b)

1000

(c)

2000

(d)

500