Saved on this device

Follow your curiosity

What discovery has been shared with you?

FACTREE gives you something interesting to discover every day — and something worth talking about together.

Start with one fact. Explore it, go deeper, then follow whichever branch catches your imagination.

Choose subjects for a surprise

Exploring any topic

Begin your discovery

Your next discovery is one click away.

Choose one or more subjects above, or leave Any Topic selected and let curiosity decide.

Mathematics

Solving Recurrence Relations via Characteristic Equations

Quick fact

The characteristic equation method transforms a linear recurrence into a polynomial, and solving that polynomial directly reveals the closed-form formula for the sequence. For the Fibonacci sequence, this yields the famous Binet formula, which involves the golden ratio.

Why this is interesting

Have you ever wondered if there's a shortcut to find the 100th Fibonacci number without adding up all the previous ones? The characteristic equation method turns that daunting task into a simple algebraic step.