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Mathematics

Recurrence Relations and Their Solutions: The Fibonacci Sequence

Quick fact

The Fibonacci sequence can be described by a simple recurrence (each term is the sum of the two before), yet it also has a closed-form formula—Binet's formula—that uses irrational numbers like √5, and the 100th Fibonacci number can be computed directly without any loop.

Why this is interesting

You’ve likely seen the Fibonacci sequence: 1, 1, 2, 3, 5, 8… But what if you could jump straight to the 100th number without computing all the previous ones?

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Recurrence Relations and Their Solutions: The Fibonacci Sequence

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