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Number Theory
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Recurrent sequences
Linear recurrent sequences
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Lucas’ sequences
Fibonacci Numbers
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The generating (power) series for Fibonacci numbers is
(1) |
Adding together
we get
,
or in other words
which yields that
(2) |
The polynomial is called the characteristic polynomial for Fibonacci numbers. Since , it has two roots , .
The number , called golden ratio . The second root .
Cite this web-page as:
Štefan Porubský: Generating Series for Fibonacci Numbers.