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[An Introduction to the Series]
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[The Rabbit Problem]
[The Rabbit Problem Proof]
[Binet's Formula]
[Binet's Formula In Action]
[The Successor Formula]
[The Successor Formula In Action]
[Binomial Form]
[Binomial Form In Action]
[Fibonacci Spiral]
[Fibonacci Spiral In Action]

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Binet's Formula

Enter a number n into the calculator below to find the nth value of the Fibonacci Series calcluated with Binet's Formula.
Fibonacci number n :
Fibonacci number f(n) :

Suppose that we want to find out what the 50th Fibonacci number is without writing out the entire series. For this we would use Binet's Formula:

We would first plug 50 in for x in the formula:

This expression then reduces as follows:

Thus we see that the 50th Fibonacci number is 12586269025. If you feel like writing and adding for a while, you can check this by calculating all previous 49 Fibonacci numbers. Of course, the formula was created in the first place so you wouldn't have to do just that!


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Random Fibonacci number from the 1st through the 200th:

 

All contents, unless otherwise specified, are © 1999 by Matt Anderson, Jeffrey Frazier, and Kris Popendorf.
Created by Team 27890 for the 1999 [ThinkQuest] competition.