continued fraction help ?

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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

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

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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