2006 Sum

Algebra Level 3

P=22221×32321×42421××20062200621 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 }

PP can Be Written as ab\frac{a}{b} Where aa and bb are coprime positive integers.

Find a+ba+b

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

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