The Maclaurin series for is

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

Problem

The Maclaurin series for arctan⁡x\arctan x is x−x33+x55−x77+…x-\dfrac{x^{3}}{3}+\dfrac{x^{5}}{5}-\dfrac{x^{7}}{7}+\dots. When this series is used to approximate arctan⁡(13)\arctan\left(\dfrac13\right) with its first four nonzero terms, calculate the maximum possible error of the approximation.

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