Which expression equals in terms of the Maclaurin coefficients of the series for a…

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

Problem

Which expression equals

f^{(k)}(0)

in terms of the Maclaurin coefficients

a_n

of the series

f(x)=\sum_{n=0}^{\infty} a_n x^{n}

for a fixed positive integer

k

? (a)

k\,a_{k-1}

(b)

a_k

(c)

k!\,a_k

(d)

\dfrac{a_k}{k!}