Infinite Geometric Series

When a geometric series has a common ratio r with |r| < 1, adding more and more terms gets closer and closer to a fixed value. This is called the sum to infinity:

S∞ = a ÷ (1 − r), valid only when |r| < 1.

If |r| ≥ 1, the series does not converge — it has no finite sum.

Find the sum to infinity, or check whether a series converges.

Continue exploring related topics:

• Geometric Sequences - Common Ratio and Exponential Growth
• Sequence Sums
• Golden Ratio - Mathematics' Most Famous Proportion