8. Let S, be a square of unit area. A ci...

8. Let S, be a square of unit area. A circle `C_1`, is inscribed in `S_1`, a square `S_2`, is inscribed in `C_1` and so on. In general, a circle `C_n` is inscribed in the square `S_n`, and then a square `S_(n+1` is inscribed in the circle `C_n`. Let `a_n` denote the sum of the areas of the circle `C_1,C_2,C_3,.....,C_n` then ` lim_(n->oo) a_n` must be

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