how to express this as finite simple continued fraction, with last term >1
12/240005
$\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}}}}}}}
$