Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.