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The Fibonacci Numbers

One special recursively defined function, which has no simple explicit definition, yields the Fibonacci numbers:


The values of this function are:


f (1)=1  
f (2)=1  
f (3)=1 + 1 = 2  
f (4)=1 + 2 = 3  
f (5)=2 + 3 = 5  
f (6)=3 + 5 = 8  
f (7)=5 + 8 = 13  
f (8)=8 + 13 = 21  
f (9)=13 + 21 = 34  
…    

Thus, the sequence of Fibonacci numbers is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, …. These numbers have many interesting properties that will be studied in higher math. They recur often in mathematics and even in nature.

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