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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
1
1
−
x
=
∑
n
=
0
∞
x
n
f(x)=\dfrac{1}{1-x}=\sum_{n=0}^{\infty} x^{n}
f
(
x
)
=
1
−
x
1
=
∑
n
=
0
∞
x
n
for
∣
x
∣
<
1
|x|<1
∣
x
∣
<
1
. Define
g
(
x
)
=
f
′
′
(
x
)
g(x)=f''(x)
g
(
x
)
=
f
′′
(
x
)
. What is the coefficient of
x
3
x^{3}
x
3
in the power series for
g
(
x
)
g(x)
g
(
x
)
? a)
4
4
4
b)
24
24
24
c)
20
20
20
d)
10
10
10
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