, which shall be named , has squares and inscribed in it. These squares form a smaller octagon, .
A regular octagonhas squares inscribed in it in the same manner, and the resulting hexagon formed is named . This pattern is repeated until infinity.
Let the area of octagon be denoted by . Given that , for some integers and , where is square-free, Find .
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Using the hint, we know that the geometric progression A 1 , A 2 , A 3 , . . . has the ratio r = 2 − 2 Therefore, the sum S = 1 − ( 2 − 2 ) 1 = 2 + 1
Hence a = 2 , b = 1 and a + b = 3