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Math Help - express number as infinite continued fraction

  1. #1
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    express number as infinite continued fraction

    \frac{11+30^{1/2}}{13}

    I know how to express a simple rational number as a continuous fraction and I could probably figure out how to handle the square root of 30 on its own but I'm not sure about this combination. Any tips or strategies? Thanks.
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  2. #2
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    Re: express number as infinite continued fraction

    Quote Originally Posted by director View Post
    \frac{11+30^{1/2}}{13}

    I know how to express a simple rational number as a continuous fraction and I could probably figure out how to handle the square root of 30 on its own but I'm not sure about this combination. Any tips or strategies? Thanks.
    This might help.
    Thanks from director
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  3. #3
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    Re: express number as infinite continued fraction

    Hello, director!

    Express as a contiued fraction: . \frac{11+\sqrt{30}}{13}

    \frac{11+\sqrt{30}}{13} \;=\;\{1,3,\overline{1,2,1,4}\}
    Thanks from director
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  4. #4
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    Re: express number as infinite continued fraction

    Quote Originally Posted by director View Post
    \frac{11+30^{1/2}}{13}

    I know how to express a simple rational number as a continuous fraction and I could probably figure out how to handle the square root of 30 on its own but I'm not sure about this combination. Any tips or strategies? Thanks.
    Have a look at this web-resource
    Thanks from director
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  5. #5
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    Re: express number as infinite continued fraction

    Thanks everyone for the answers/links. I was about to work out the answer using these resources.
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