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=== Limit of consecutive quotients ===
[[Johannes Kepler]] observed that the ratio of consecutive Fibonacci numbers [[convergent sequence|converges]]. He wrote that "as 5 is to 8 so is 8 to 13, practically, and as 8 is to 13, so is 13 to 21 almost", and concluded that these ratios approach the golden ratio <math>\varphi
<math display=block>\lim_{n\to\infty}\frac{F_{n+1}}{F_n}=\varphi.</math>
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