Geometric Series
Free Geometric Series calculator with clear step-by-step results.
About Geometric Series
Sums the terms of a geometric series, finite or converging infinite.
Formula
Formula
Sum = a(1−rⁿ)/(1−r); infinite = a/(1−r) when |r|<1
Worked example
With the default values below, Geometric Series returns Sum of Series of 1.9980. Change any input above and every figure here is recalculated in your browser.
Inputs used
- First termminimum 0
- 1
- Common ratiominimum 0
- 0.5
- Number of termsminimum 1
- 10
Results
- Sum of Series
- 1.9980
- Infinite Sum (if |r|<1)
- 2.0000
- Ratio
- 0.500
Step by step
- 1Values used
- 2Formula
- 3Sum of Series= 1.9980
- 4Infinite Sum (if |r|<1)= 2.0000
- 5Ratio= 0.500
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
How does this calculator work?
Sums the terms of a geometric series, finite or converging infinite.
Why does this matter?
The infinite sum requires |r| < 1.