Permalink Submitted by R. Mashlan on November 30, 2021

Yes you can. This is because any linear recurrent sequence such as the Fibonacci sequence approaches proportionality to the Golden Ratio raised to the nth power for the nth term (see Binet's formula for generalized linear recurrent sequences). This was conjectured by Johannes Kepler in Harmonics Mundi, published in 1619, and even earlier by a lesser known German mathematician Simon Jacobs.

## Approximation to a fraction

Yes you can. This is because any linear recurrent sequence such as the Fibonacci sequence approaches proportionality to the Golden Ratio raised to the nth power for the nth term (see Binet's formula for generalized linear recurrent sequences). This was conjectured by Johannes Kepler in Harmonics Mundi, published in 1619, and even earlier by a lesser known German mathematician Simon Jacobs.