Let ( f n ) n ∈ N {\displaystyle {}{\left(f_{n}\right)}_{n\in \mathbb {N} }} be the sequence of the Fibonacci numbers and
Prove that this sequence converges in R {\displaystyle {}\mathbb {R} } and that its limit x {\displaystyle {}x} satisfies the relation
Calculate this x {\displaystyle {}x} .