Fibonacci numbers in closed form
Posted: Posted November 19th, 2017Edited November 19th, 2017 by The Fly
You all know the Fibonacci numbers, which we'll label as a function like this:
\(F(0) = 1, \quad F(1) = 1, \quad F(2) = 2, \quad F(3) = 3, \quad F(4) = 5, \quad F(5) = 8, \quad F(6) = 13, \dots \)
Each number is the sum of the previous two. According to this notation, the 5th Fibonacci number is 8.
Without looking it up anywhere on the internet (nor wiki or anywhere), can you obtain and write down a closed form for the nth Fibonacci number -- i.e., a closed formula that gives you \(F(n)\) directly (without reference to the previous two numbers)?
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