How would I find the continued fraction of and number $a/b$? For example, $5/8$ = $1/(1+3/5)$ I tried using its decimal expansion but couldn’t find anything, and I want to be able to describe the golden ratio as a fraction.
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1... just continue the process to get the continued fraction expansion of $5/8$, so $5/8=1/(8/5)=1/(1+3/5)=1/(1+1/(5/3))=1/(1+1/(1+2/3))=1/(1+1/(1+1+(3/2)))=1/(1+1/(1+1+(1+1/2)))=[0;1, 1, 1, 2]$. The golden ratio is in this sense using the Fibonacci sequence $[0;1,1,1,1,\dots]$ . – dan_fulea Sep 20 '18 at 14:50
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Thank you so much – Jon due Sep 20 '18 at 15:17