Which of the following gives the Maclaurin series representation of ?

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

Problem

Which of the following gives the Maclaurin series representation of

\cos(4x)

? (a)

\displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{16^{\,n} x^{2n}}{(2n)!}

(b)

\displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{4^{\,n} x^{2n}}{(2n)!}

(c)

\displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{16^{\,n} x^{2n+1}}{(2n+1)!}

(d)

\displaystyle \sum_{n=0}^{\infty} (-1)^{n}\,\dfrac{16^{\,n} x^{2n}}{n!}