Simplifying the Fraction
Source:
July 27, 2008
Problem Statement
Simplify
\left(\frac {1 \cdot 2 \cdot 4 \plus{} 2 \cdot 4 \cdot 8 \plus{} \cdots \plus{} n \cdot 2n \cdot 4n}{1 \cdot 3 \cdot 9 \plus{} 2 \cdot 6 \cdot 18 \plus{} \cdots \plus{} n \cdot 3n \cdot 9n}\right)^{\frac {1}{3}}