Let be the th partial sum of the series for

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

Problem

Let

S_N = \displaystyle \sum_{n=0}^{N}(-1)^n\frac{0.6^{2n+1}}{2n+1}

be the

N

th partial sum of the series for

\arctan(0.6)

. What is the least value of

N

for which

|\arctan(0.6)-S_N|<10^{-5}

? (a)

N=8

(b)

N=7

(c)

N=6

(d)

N=9