anthyphairetic ratio
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a) Show that the anthyphairetic ratio [x:1] is [1, 1, 1,...]
**b**) Let a_n be the ratio expressed by the anthyphairetic ratio [1,...,1,2] where there are n ones followed by a 2. Explain why, as n grows, a_n gets closer and closer to [x:1]. In this respect, the entries in an anthyphairetic ratio are like the digits in a decimal expansion.
c) You may wonder why we do not look at the anthyphairetic ratios [1,...,1,1]: in other words, why the 2 at the end? Explain why the 2 at the end is necessary.
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Suppose (please see the attached file) is the positive root of (please see the attached file)
a) Show that the anthyphairetic ratio (please see the attached file) is (please see the attached file)
b) Let (please see the attached file) be the ratio expressed by the anthyphairetic ratio [1,...,1,2] where there are (please see the attached file) ones followed by a 2. Explain why, as (please see the attached file) grows, (please see the attached file) gets closer and closer to (please see the attached file). In this respect, the entries in an anthyphairetic ratio are like the digits in a decimal expansion.
c) You may wonder why we do not look at the anthyphairetic ratios [1,...,1,1]: in other ...
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