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Mathlib.Analysis.SpecificLimits.Fibonacci

The ratio of consecutive Fibonacci numbers #

We prove that the ratio of consecutive Fibonacci numbers tends to the golden ratio.

The limit of fib (n + 1) / fib n as n → ∞ is the golden ratio.

The limit of fib n / fib (n + 1) as n → ∞ is the negative conjugate of the golden ratio.