The Maclaurin series of can be written in the form

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

Problem

The Maclaurin series of

\dfrac{\arctan x}{x}

can be written in the form

\displaystyle\sum_{n=0}^{\infty} c_n x^{2n}

. Which of the following gives

c_n

in closed form? (a)

c_n = \dfrac{(-1)^{n}}{(2n+1)!}

(b)

c_n = \dfrac{(-1)^{n}}{2n-1}

(c)

c_n = \dfrac{(-1)^{n}}{2n+1}

(d)

c_n = \dfrac{(-1)^{n+1}}{2n+1}