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Math Help - Infinite summations: area of polygon

  1. #1
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    Infinite summations: area of polygon

    The vertices of a polygon are:

    (-1,0), \ (-1+2^{-n},1-(-1+2^{-n})^{2}), \ (-1+2 \cdot 2^{-n},1-(-1+2\cdot2^{-n})^{2}), \ (-1+3\cdot2^{-n},1-(-1+3\cdot2^{-n})^{2}), ...,(1,0)

    I have to show that the area of the polygon is 1 + 4^(-1) + 4^(-2) + ... + 4^(-n).

    How would I go about doing that? Not sure how to proceed.
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    Re: Infinite summations: area of polygon

    Quote Originally Posted by BrownianMan View Post
    The vertices of a polygon are:

    (-1,0), \ (-1+2^{-n},1-(-1+2^{-n})^{2}), \ (-1+2 \cdot 2^{-n},1-(-1+2\cdot2^{-n})^{2}), \ (-1+3\cdot2^{-n},1-(-1+3\cdot2^{-n})^{2}), ...,(1,0)

    I have to show that the area of the polygon is 1 + 4^(-1) + 4^(-2) + ... + 4^(-n).

    How would I go about doing that? Not sure how to proceed.
    Use the Polygon - Wikipedia, the free encyclopedia formula.
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  3. #3
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    Re: Infinite summations: area of polygon

    I tried using it and could not get the answer.
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    Re: Infinite summations: area of polygon

    Quote Originally Posted by BrownianMan View Post
    The vertices of a polygon are:

    (-1,0), \ (-1+2^{-n},1-(-1+2^{-n})^{2}), \ (-1+2 \cdot 2^{-n},1-(-1+2\cdot2^{-n})^{2}), \ (-1+3\cdot2^{-n},1-(-1+3\cdot2^{-n})^{2}), ...,(1,0)

    I have to show that the area of the polygon is 1 + 4^(-1) + 4^(-2) + ... + 4^(-n)
    I don't know how in the world anyone can read the above.
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    Re: Infinite summations: area of polygon

    What's wrong with it?
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    Re: Infinite summations: area of polygon

    Does anyone have any idea on how to solve this? I tried using the formula for the general polygon, but I can't get 1 + 4^(-1) + 4^(-2) + ... + 4^(-n) for the area.
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