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Mathematics
Mathematics
Problem
Let
h
(
x
)
=
∑
n
=
0
∞
3
n
n
+
2
(
x
+
1
)
n
h(x)=\displaystyle \sum_{n=0}^{\infty} \frac{3^{n}}{n+2}\,(x+1)^{n}
h
(
x
)
=
n
=
0
∑
∞
n
+
2
3
n
(
x
+
1
)
n
. For any non-negative integer
k
k
k
, derive a formula for
h
(
k
)
(
−
1
)
h^{(k)}(-1)
h
(
k
)
(
−
1
)
expressed in terms of
k
k
k
.
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