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    Sum of infinite geometric series

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    A regular hexagon is inscribed in a circle of radius 100. The area of that hexagon outside the square is shaded. Another circle is inscribed in the hexagon, and hexagon is inscribed in the second circle. The area of the second circle which lies outside the hexagon is shaded. This process continues to infinity.
    What is the sum of all shaded areas?

    Radius of 1 = 100
    Radius of 2 = ______
    Radius of 3 = _______
    Radius of 4 = ________
    Side of hexagon 1st =_________
    Side of hexagon 2nd = ________
    Side of hexagon 3rd = ________
    Side of hexagon 4th = _______
    Area of Circle 1 = ________
    Area of Circle 2 = ________
    Area of Crcle 3 =________
    Area of Circle 4 = _______
    Area of Hexagon 1 = _______
    Area of Hexagon 2 =______
    Area of Hexagon 3 = ______
    Area of Hexagon 4 = _________
    Difference of 1st =_________
    Difference of 2nd =_________
    Difference of 3rd =_________
    Difference of 4th =________

    Each new one is _________of the previous area.
    Sum of all areas = ___________

    Is there any relationship concerning the areas as the number of sides of the inscribed figure increases? If so what would you predict would be the area sum for 8 or 9 sides?_________

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    https://brainmass.com/math/algebraic-geometry/sum-infinite-geometric-series-40905

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    The sum of an infinite Geometric Series
    ________________________________________
    A regular hexagon is inscribed in a circle of radius 100. The area of that hexagon outside the square is shaded. Another circle is inscribed in the hexagon, and hexagon is inscribed in the second circle. The area of the second circle which lies outside the hexagon is shaded. This ...

    Solution Summary

    This is an infinite geometric series question using the hexagons and circles inscribed inside of each other.

    $2.49

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