Using the first four nonzero terms of the Maclaurin series

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

Problem

\displaystyle\arctan x =\sum_{n=0}^{\infty}(-1)^{n}\dfrac{x^{2n+1}}{2n+1}

, form an interval that is guaranteed to contain

\dfrac{\pi}{4}

. Express both bounds as exact rational numbers.