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

12/240005

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- May 10th 2008, 07:53 AMRakeshcontinued fraction help ?
how to express this as finite simple continued fraction, with last term >1

12/240005 - May 10th 2008, 08:09 AMMoo
- May 10th 2008, 08:10 AMPaulRS
$\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}}}}}}}

$