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SE-SKOLORNAS 1966 Problem 4

    Let f(x)=1+2xf(x) = 1 + \frac{2}{x} . Put f1(x)=f(x)f_1(x) = f(x) , f2(x)=f(f1(x))f_2(x) = f(f_1(x)) , f3(x)=f(f2(x))f_3(x) = f(f_2(x)) , ...... . Find the solutions to x=fn(x)x = f_n(x) for n>0n > 0 .

    Dataset text AI-MO AoPS. Quoted with source.

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