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Mathematics

Solving Recurrence Relations with Characteristic Equations

Quick fact

The Fibonacci sequence, defined by F(n) = F(n-1) + F(n-2), can be expressed with Binet's formula, which involves powers of (1+√5)/2 and (1−√5)/2—an explicit solution derived from a characteristic equation.

Why this is interesting

Can you find the 100th number in the Fibonacci sequence without listing all 99 before it? Recurrences may seem to require step-by-step calculation, but characteristic equations unlock a direct formula.