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Math Help - 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
    \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}}}
    =\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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    <br />
\frac{{12}}<br />
{{240005}} = \frac{1}<br />
{{\tfrac{{240005}}<br />
{{12}}}} = \frac{1}<br />
{{\tfrac{{240000 + 5}}<br />
{{12}}}} = \frac{1}<br />
{{20000 + \tfrac{5}<br />
{{12}}}}<br />

    And: <br />
\tfrac{5}<br />
{{12}} = \frac{1}<br />
{{\tfrac{{12}}<br />
{5}}} = \frac{1}<br />
{{2 + \tfrac{2}<br />
{5}}} = \frac{1}<br />
{{2 + \tfrac{1}<br />
{{\tfrac{5}<br />
{2}}}}} = \frac{1}<br />
{{2 + \tfrac{1}<br />
{{2 + \tfrac{1}<br />
{2}}}}}<br />

    Thus: <br />
\frac{{12}}<br />
{{240005}} = \frac{1}<br />
{{20000 + \frac{1}<br />
{{2 + \tfrac{1}<br />
{{2 + \tfrac{1}<br />
{2}}}}}}}<br />
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