Let $C_0$ be a circle of radius $I$ . For $n \geq 1$, let $C_n$ be a circle whose area equals the area of a square inscribed in $C_{n-1} .$ Then, $\sum \limits_{i=0}^{\infty}$ Area $\left(C_i\right)$ equals

  • [KVPY 2014]
  • A

    $\pi^2$

  • B

    $\frac{\pi-2}{\pi^2}$

  • C

    $\frac{1}{\pi^2}$

  • D

    $\frac{\pi^2}{\pi-2}$

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