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Mathematics
Mathematics
Problem
For
k
∈
N
k \in \mathbb{N}
k
∈
N
, let
1
α
(
α
+
1
)
(
α
+
2
)
…
(
α
+
20
)
=
∑
k
=
0
20
A
k
α
+
k
\frac{1}{\alpha(\alpha+1)(\alpha+2)\dots(\alpha+20)} = \sum_{k=0}^{20} \frac{A_k}{\alpha+k}
α
(
α
+
1
)
(
α
+
2
)
…
(
α
+
20
)
1
=
k
=
0
∑
20
α
+
k
A
k
where
α
>
0
\alpha > 0
α
>
0
. Then the value of
100
(
A
14
+
A
15
A
13
)
2
100 \left( \frac{A_{14} + A_{15}}{A_{13}} \right)^2
100
(
A
13
A
14
+
A
15
)
2
is equal to ____.
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