Grade 12 · Theory
Infinite series
Sequences and series · about 3 min
Visual overview: Infinite series1 MIN READ
2 study sections · pause after each one and recall the key ideaSome infinite geometric series settle on a finite total; others grow without limit.
Key points- An infinite geometric series converges only when −1 < r < 1.
- Sum to infinity: S∞ = a/(1 − r).
- If |r| ≥ 1 the series diverges and has no sum.
- Convergence questions often ask for the values of x that make |r| < 1.
- Converge — approach a finite total.
- Diverge — grow without bound.
EXAM TIP
state the condition −1 < r < 1 explicitly before using S∞; it is a marked step.