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Solving the Fibonacci recurrence with generating functions
posted by
benzi
posted 1y 59d ago
In straight numbers, that's
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Wrap equations in [EQ]equation here[/EQ] tags, and inline equations in [IEQ][/IEQ] tags.
In straight numbers, that's [eq]F_n = \frac{1}{\sqrt{5}} \left[ \left(\frac{1 + \sqrt{5}}{2}\right)^n - \left(\frac{1 - \sqrt{5}}{2}\right)^n \right].[/eq]
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![F_n = \frac{1}{\sqrt{5}} \left[ \left(\frac{1 + \sqrt{5}}{2}\right)^n - \left(\frac{1 - \sqrt{5}}{2}\right)^n \right].](equations/15740_0.png "F_n = \frac{1}{\sqrt{5}} \left[ \left(\frac{1 + \sqrt{5}}{2}\right)^n - \left(\frac{1 - \sqrt{5}}{2}\right)^n \right].")