Let be the sum of the alternating harmonic series

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

Problem

Let

S

be the sum of the alternating harmonic series

\displaystyle \sum_{k=1}^{\infty} \dfrac{(-1)^{k+1}}{k}

. If

S_{50}

denotes the 50th partial sum, which of the following is the greatest possible value of

|S-S_{50}|

? (a)

\displaystyle \frac{2}{51}\approx 0.0392

(b)

\displaystyle \frac{1}{51}\approx 0.0196

(c)

\displaystyle \frac{1}{50}=0.02

(d)

\displaystyle \frac{1}{102}\approx 0.0098