Fibonacci, 2018 and me.

Let $(a_{n})_{n \ge 1}$ be the sequence defined by the following recurrence relation: $a_1 = 2018, \space a_2 = 2018$ and $a_n = a_{n - 1} + a_{n - 2}$ for all natural number $n \ge 3$ . Then, there exists a positive real number $a$ such that the limit $\displaystyle S_k = \lim_{n \to \infty} \frac{a_n}{k^n}$ converges if $k$ is a positive real number such that $k \ge a$ , and $S_k$ diverges if $k$ is a positive real number such that $k < a$ .

• Enter $\displaystyle \lim_{n \to \infty} \frac{a_n}{a^n}$