Circle!

Geometry Level 3

Let \(C_0\) be a unit circle. For \(n\geq 1\), let \(C_n\) be a circle whose area equals the area of a square inscribed in \(C_{n-1}\), where \(n=1,2,3,\ldots\).

Compute \[ \large \sum_{i=1}^{\infty}\text{Area}(C_i) \; . \]

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