Get stuck with many inscribed shapes

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a circle inscribed in a square , the square inscribed inside a circle , the circle inscribed in a square , the square inscribed inside a circle , down to n n number of inscribed squares and circles . PS :- n n is the number of circles . what is the ratio of the area of biggest circle to the area of the smallest circle.

2 n 1 2^{n-1} ( 2 ) 2 n + 1 (\sqrt 2)^{2n+1} 2 . 2 n 1 \sqrt 2.2^{n-1} 2 n 2^n

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