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2005 AIME Problems
7
A Giant Expansion
A Giant Expansion
Source:
November 13, 2005
AMC
AIME
Problem Statement
Let
x
=
4
(
5
+
1
)
(
5
4
+
1
)
(
5
8
+
1
)
(
5
16
+
1
)
.
x=\frac{4}{(\sqrt{5}+1)(\sqrt[4]{5}+1)(\sqrt[8]{5}+1)(\sqrt[16]{5}+1)}.
x
=
(
5
+
1
)
(
4
5
+
1
)
(
8
5
+
1
)
(
16
5
+
1
)
4
.
Find
(
x
+
1
)
48
(x+1)^{48}
(
x
+
1
)
48
.
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