Math 2.0

Number theory Fact

Fibonacci recurrence

Builds on Fibonacci sequence

Statement

Let nn be a natural number, and let FmF_m be the Fibonacci numbers. Then Fn+2=Fn+1+Fn.F_{n+2} = F_{n+1} + F_n.

Remarks

With the values F0=0F_0 = 0 and F1=1F_1 = 1, the recurrence determines the whole sequence. The recurrence extends to negative indices with F−n=(−1)n+1FnF_{-n} = (-1)^{n+1} F_n.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first.

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Fibonacci sequence, example, no evidence levelFibonacci sequenceexampleFibonacci recurrence, statement, no evidence levelFibonacci recurrencestatement
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  1. Fibonacci sequence example
  2. Fibonacci recurrence statement

Further reading

  1. Web https://en.wikipedia.org/wiki/Fibonacci_sequence, Definition
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Kindstatement, fact
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MSC11B39
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UsesFibonacci sequence

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