For , the remainder after terms of the Maclaurin series satisfies when . Determine…

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

Problem

For

f(x)=\ln(1+x)

, the remainder after

n

terms of the Maclaurin series satisfies

|R_{n}(x)|\le \dfrac{|x|^{\,n+1}}{n+1}

when

|x|\le 0.2

. Determine the smallest integer

n

for which

|R_{n}(0.2)|\le 10^{-4}