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Thread: continued fraction help ?

  1. #1
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    continued fraction help ?

    how to express this as finite simple continued fraction, with last term >1

    12/240005
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  2. #2
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    Hello,

    Quote Originally Posted by Rakesh View Post
    how to express this as finite simple continued fraction, with last term >1

    12/240005
    $\displaystyle \frac{12}{240005}=\frac{1}{\dfrac{240005}{12}}=\fr ac{1}{20000+\dfrac{5}{12}}=\frac{1}{20000+\dfrac{1 }{\dfrac{12}{5}}}=\frac{1}{20000+\dfrac{1}{2+\frac {2}{5}}}$
    $\displaystyle =\frac{1}{20000+\dfrac{1}{2+\dfrac{1}{\frac{5}{2}} }}$

    etc...
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  3. #3
    Super Member PaulRS's Avatar
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    $\displaystyle
    \frac{{12}}
    {{240005}} = \frac{1}
    {{\tfrac{{240005}}
    {{12}}}} = \frac{1}
    {{\tfrac{{240000 + 5}}
    {{12}}}} = \frac{1}
    {{20000 + \tfrac{5}
    {{12}}}}
    $

    And: $\displaystyle
    \tfrac{5}
    {{12}} = \frac{1}
    {{\tfrac{{12}}
    {5}}} = \frac{1}
    {{2 + \tfrac{2}
    {5}}} = \frac{1}
    {{2 + \tfrac{1}
    {{\tfrac{5}
    {2}}}}} = \frac{1}
    {{2 + \tfrac{1}
    {{2 + \tfrac{1}
    {2}}}}}
    $

    Thus: $\displaystyle
    \frac{{12}}
    {{240005}} = \frac{1}
    {{20000 + \frac{1}
    {{2 + \tfrac{1}
    {{2 + \tfrac{1}
    {2}}}}}}}
    $
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