# 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

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

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

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