HMMT 2006 F2

Find

$\frac{2^{2}}{2^{2}-1} \cdot \frac{3^{2}}{3^{2}-1} \cdot \frac{4^{2}}{4^{2}-1} \cdots \cdots \frac{2006^{2}}{2006^{2}-1}$

Dataset text NuminaMath olympiads. Quoted with source.

Solutions

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