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My intention for this article is to provide a look into how the decimal expansion of some fractions yields the Fibonacci sequence by Krishnan in Cantor’s Paradise.
Let us first take a look at the decimal expansion of 1/89:
Now, for a quick refresher on the Fibonacci sequence. You start with the numbers 0 and 1, and every number after that is the sum of the two before it. This gives us the sequence: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144…
(A small note on notation: Fₙ = Fib(n) = nth Fibonacci number)...
Benefits
This method of calculating the nth Fibonacci number can be computed in the same speed as the fastest known method(Matrix Exponentiation). Also, this is a super interesting way of finding the nth Fibonacci number, because unlike
Source: Medium
