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Continued fraction convergents

  1. Oct 29, 2011 #1
    Hi, I think I have the first part of the question correct but can't seem to get the second so any help would be fantastic.

    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.
  2. jcsd
  3. Oct 29, 2011 #2
    2.0000000000000 = 2
    3.0000000000000 = 3
    2.7500000000000 = 11/4
    2.8000000000000 = 14/5
    2.7948717948718 = 109/39 = 327/117
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