Problem 46003. Compute Khinchin's constant

Khinchin's constant K_0 = 2.684542001... (also written "Khintchine's constant") has the amazing property that it is the limiting value of the geometric mean of the partial quotients from a continued fraction expansion of almost all numbers. In other words, if a number x is expanded as
Continued fraction expansion of x
then as n approaches infinity
K_0 is the nth root of the product of a_1 through a_n
Compute Khinchin's constant. The test suite will check for a difference of 10^{-12}.
Solve

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36.0% Correct | 64.0% Incorrect
Last Solution submitted on Jul 15, 2024

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