802 years ago, a book (Liber abaci) was published that was written by a man named Leonardo Fibonacci. There was an interesting problem contained in this book that had to do with the growth of a rabbit population. The values of the amount of rabbit pairs at consecutive months gave birth to the following sequence:
1, 1, 2, 3, 5, 8, 13, 21, …
The recursive formula for it is:
We also have an explicit formula for this sequence and this is:
Your task is to study what happens to the ratio:
As it travels further and further along
the sequence i.e.
?
HINT:
Your quest is to calculate:
Take into account that
.
What happens to such numbers if they are multiplied over and over
again? Where are they heading to?