Which of the following power series equals for all real ?

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

Problem

Which of the following power series equals

\sin x

for all real

x

? (a)

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

(b)

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

(c)

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

(d)

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