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Let $(f_n)$ be the fibonacci sequence and let $x_n = \dfrac{f_{n+1}}{f_n}$. Given that $\lim_{n \to \infty}(x_n) = L$ exists, determine the value of $L$.

rlartiga
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priya
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  • This appears to have been asked and answered here: http://math.stackexchange.com/questions/739229/fibonacci-sequence-golden-ratio – David K Sep 09 '14 at 15:41

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A start: We have $f_{n+1}=f_n+f_{n-1}$. Divide both sides by $f_n$. We obtain $$x_n=1+\frac{1}{x_{n-1}}.$$

André Nicolas
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