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Q: Express [tex]\frac{327}{117}[/tex] as a continued fraction and find the convergents of it.

My working:

[tex]\frac{327}{117}=2 +\frac{93}{117} =2+\frac{1}{\frac{117}{93}}[/tex]

[tex]\frac{117}{93}=1 + \frac{24}{93} =1+\frac{1}{\frac{93}{24}}[/tex]

I continue like this to finally get:

[tex]\frac{327}{117}=2 + \frac{1}{1+ \frac{1}{3+\frac{1}{1+\frac{1}{7}}}}[/tex].

I think it is right, but I can't get the second part at all.

Thanks for any help.