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 Recurrences via Generating Functions

Quick fact

One elegant trick: the Fibonacci sequence, defined by the recurrence Fₙ = Fₙ₋₁ + Fₙ₋₂, can be encoded in a single function. From that function, you can read off an exact formula for Fₙ without computing any previous terms.

Why this is interesting

Have you ever seen a pattern like 1, 1, 2, 3, 5, 8… and wondered, 'What comes next?' But could you find the 100th number without adding up all the previous ones?