Mathematics

Mathematics

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

.

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