# continued fraction help ?

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

12/240005
• May 10th 2008, 08:09 AM
Moo
Hello,

Quote:

Originally Posted by Rakesh
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...
• May 10th 2008, 08:10 AM
PaulRS
$
\frac{{12}}
{{240005}} = \frac{1}
{{\tfrac{{240005}}
{{12}}}} = \frac{1}
{{\tfrac{{240000 + 5}}
{{12}}}} = \frac{1}
{{20000 + \tfrac{5}
{{12}}}}
$

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