My earlier blog about the Fibonacci series gets a lot of hits, so I thought I would write something more, as clearly there is interest.
Let and . Then .
(3) Simplifying (2)
(4) Simplifying further – from (1):
(6) We know that so we can restate (5) as
But also and (7) can be restated as
In other words, .
- Something interesting about Fibonacci numbers (cartesianproduct.wordpress.com)
- Numbers in Nature – the Movie (delamagente.wordpress.com)