Let . Which statement correctly describes the coefficient of in the series for…

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

Problem

Let

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

. Which statement correctly describes the coefficient of

x^{n}

in the series for

x^{3}f(x)

? (a) It equals

a_{n-3}

for

n\ge 3

and

0

for

n<3

. (correct) (b) It equals

a_{n+3}

for all

n\ge 0

. (c) It equals

3a_{n}

for all

n\ge 0

. (d) It equals

0

for

n<3

and

3a_{n-3}

for

n\ge 3