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Mathematics

Using Generating Functions to Solve Recurrence Relations

Quick fact

By encoding a recurrence as a power series, you can solve it with algebra. For example, the Fibonacci sequence’s generating function is x/(1 - x - x²), from which you can derive Binet’s formula.

Why this is interesting

What if you could turn a sequence like 1, 1, 2, 3, 5, 8… into a single algebraic expression and then just read off any term? Generating functions make this magic happen.