Let for . Define . What is the coefficient of in the power series for…

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

Problem

Let

f(x)=\dfrac{1}{1-x}=\sum_{n=0}^{\infty} x^{n}

for

|x|<1

. Define

g(x)=f''(x)

. What is the coefficient of

x^{3}

in the power series for

g(x)

? (a)

4

(b)

24

(c)

20

(d)

10