Skip to content
Free public beta until December 4, 2026: every course is open, no card needed. After that, the first chapter of each course stays free and full access is a one-time $39 ($19 for up to 100 founding members chosen for helpful feedback). Your progress is kept. How the beta works

geometric series

A sum where each term is a fixed ratio times the one before it.

\sum_{k=0}^{\infty} ar^k converges to \frac{a}{1-r} exactly when |r| < 1; it diverges otherwise.

Read the full section →
Graph settings

Calculator