The series converges for

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

Problem

The series

\ln(1+x)=x-\dfrac{x^{2}}{2}+\dfrac{x^{3}}{3}-\dfrac{x^{4}}{4}+\cdots

converges for

-1<x\le 1

. When

x=0.3

, which of the following represents the smallest integer

n

such that the polynomial obtained by truncating after the

x^{n}

term approximates

\ln(1+0.3)

with error magnitude less than

0.001

? (a)

n=3

(b)

n=4

(c)

n=2

(d)

n=5