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4
2007 Algebra #4: Telescoping Product
2007 Algebra #4: Telescoping Product
Source:
June 21, 2012
Problem Statement
Compute
2
3
−
1
2
3
+
1
⋅
3
3
−
1
3
3
+
1
⋅
4
3
−
1
4
3
+
1
⋅
5
3
−
1
5
3
+
1
⋅
6
3
−
1
6
3
+
1
.
\dfrac{2^3-1}{2^3+1}\cdot\dfrac{3^3-1}{3^3+1}\cdot\dfrac{4^3-1}{4^3+1}\cdot\dfrac{5^3-1}{5^3+1}\cdot\dfrac{6^3-1}{6^3+1}.
2
3
+
1
2
3
−
1
⋅
3
3
+
1
3
3
−
1
⋅
4
3
+
1
4
3
−
1
⋅
5
3
+
1
5
3
−
1
⋅
6
3
+
1
6
3
−
1
.
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