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7
2009 Algebra #7 - Find Product
2009 Algebra #7 - Find Product
Source:
January 2, 2012
Problem Statement
Simplify the product
∏
m
=
1
100
∏
n
=
1
100
x
n
+
m
+
x
n
+
m
+
2
+
x
2
n
+
1
+
x
2
m
+
1
x
2
n
+
2
x
n
+
m
+
x
2
m
\prod_{m=1}^{100}\prod_{n=1}^{100}\frac{x^{n+m}+x^{n+m+2}+x^{2n+1}+x^{2m+1}}{x^{2n}+2x^{n+m}+x^{2m}}
m
=
1
∏
100
n
=
1
∏
100
x
2
n
+
2
x
n
+
m
+
x
2
m
x
n
+
m
+
x
n
+
m
+
2
+
x
2
n
+
1
+
x
2
m
+
1
Express your answer in terms of
x
x
x
.
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