Question

Fun fibonacci sequence problem: show that

\[\dfrac{F_{n+1}}{F_n} =1+
\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{1+\dfrac{1}{\ddots \text{n times}{}}}}}\]

Answer 1

\[1, 1, 2, 3, 5, 8, ... \]

examples :
\(\dfrac{F_{1+1}}{F_1} = 1\)

\(\dfrac{F_{2+1}}{F_2} = 1+\dfrac{1}{1}\)

\(\dfrac{F_{3+1}}{F_3} = 1+\dfrac{1}{1+\dfrac{1}{1}}\)