The power series for is for

MATHEMATICS · Subjective · AP · Calculus BC · Infinite Sequences and Series · Infinite Sequences and Series

Problem

The power series for

\ln(1+x)

x-\dfrac{x^{2}}{2}+\dfrac{x^{3}}{3}-\dfrac{x^{4}}{4}+\cdots

for

-1<x\le 1

. For

x=0.6

, determine the least integer

n

such that using the first

n

non-zero terms yields an approximation to

\ln(1.6)

whose error does not exceed

10^{-5}