system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How does the golden ratio follow the fibonacci sequence?
gpt
Take two successive numbers of Fibonacci sequence, 13 and 21 for example. 21/13 will be close to golden ratio. Kepler proved that limit of ratio of two infinitely large successive Fibonacci numbers is golden ratio, or lim{n -> inf} F{n+1}/Fn = phi.

EDIT: More general form, as wikipedia says, is lim{n -> inf} F{n+a}/Fn = phi^a, and it leads to phi^{n+1} = phi^n + phi^{n-1}.