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Geometric Series Finite Sum Calculator

S_n = a · (1 − rⁿ) / (1 − r) for r ≠ 1; S_n = n · a for r = 1.

Compute the sum of the first n terms of a geometric series with first term a and common ratio r: S_n = a · (1 − rⁿ) / (1 − r) for r ≠ 1. The calculator handles the r = 1 special case by returning n · a, and reports both the partial sum and (if |r| < 1) the limit S_∞ = a / (1 − r).

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

S_n = a · (1 − rⁿ) / (1 − r); S_∞ = a / (1 − r) if |r| < 1.

In depth

Compute the sum of the first n terms of a geometric series with first term a and common ratio r: S_n = a · (1 − rⁿ) / (1 − r) for r ≠ 1. The calculator handles the r = 1 special case by returning n · a, and reports both the partial sum and (if |r| < 1) the limit S_∞ = a / (1 − r).