2006 Sum

Algebra Level 3

\[ P= \frac{2^2}{2^2 -1 } \times \frac{3^2}{3^2 - 1} \times \frac{4^2}{4^2 - 1}\times \cdot \cdot \cdot \times \frac{2006^2}{2006^2 - 1 }\]

\(P\) can Be Written as \(\frac{a}{b}\) Where \(a\) and \(b\) are coprime positive integers.

Find \(a+b\)

Note: This question was posed in the 2006 Harvard MIT Math Tournament

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