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.