Total area of squares

Suppose in Fig. 6 we begin with a square with sides of length 1 (area = 1) and construct another square inside by connecting the midpoints of the sides. Then the new square has area 1/2. If we continue the process of constructing each new square by connecting the midpoints of the sides of the previous square, we get a sequence of squares each of which has 1/2 half the area of the previous square. Find the total area of all of the squares….

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