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Mathematics
Mathematics
Problem
Let
f
(
x
)
=
∑
n
=
0
∞
(
−
1
)
n
n
+
1
(
x
−
2
)
n
+
2
f(x)=\displaystyle \sum_{n=0}^{\infty} \frac{(-1)^{n}}{n+1}\,(x-2)^{n+2}
f
(
x
)
=
n
=
0
∑
∞
n
+
1
(
−
1
)
n
(
x
−
2
)
n
+
2
. Determine the coefficient of
(
x
−
2
)
4
(x-2)^4
(
x
−
2
)
4
in the power series for
f
′
(
x
)
f'(x)
f
′
(
x
)
.
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