Let be the sum of the first four nonzero terms of the series

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

Problem

Let

P=\displaystyle\sum_{k=2}^{5}\frac{1}{k(\ln k)^2}

be the sum of the first four nonzero terms of the series

\displaystyle S=\sum_{k=2}^{\infty}\frac{1}{k(\ln k)^2}

. Which interval must contain

S

? (a)

1.96 < S < 2.02

(b)

2.22 < S < 2.29

(c)

2.08 < S < 2.15

(d)

2.14 < S < 2.20