Sum of Geometric Series
Sₙ = a₁(1 − rⁿ) / (1 − r) for r ≠ 1. Infinite: S∞ = a₁/(1−r) if |r|<1.
Result
General calculation reads
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How to use this calculator
- Enter a₁, r, and n.
- Use n=0 for infinite series (only valid |r|<1).
About this calculator
Sum of finite geometric series: Sₙ = a₁(1 − rⁿ)/(1 − r). Infinite series only converges if |r| < 1: S∞ = a₁/(1−r). Examples: Zeno's paradox (1 + ½ + ¼ + ... = 2), present value of perpetuity in finance (CF/r), exponential decay totals. The formula is a cornerstone of finance, probability, and physics (geometric distribution).
Frequently asked
Why a₁/(1−r) for infinite?+
Why diverge if |r|≥1?+
Zeno's paradox?+
Perpetuity?+
Repeating decimals?+
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