Interesting Relations?

Number Theory Level 2

True or False (or Ambiguous)?

t h e n t h L u c a s n u m b e r t h e n t h F i b o n a c c i n u m b e r \dfrac{the \ nth \ Lucas \ number}{the \ nth \ Fibonacci \ number} tends to 5 \sqrt{5}

Note : You may check the wikis for clarification

False Ambiguous True

Mohammad Farhat by Mohammad Farhat , 16, Singapore

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1 solution

The convergence is quite rapid. By n = 100 n=100 , the error is less than 5.E-418.

lim n → ∞ L n F n ⇒ 5 \underset{n\to \infty }{\text{lim}}\frac{L_n}{F_n} \Rightarrow \sqrt{5}

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