About the Infinite Geometric Series Calculator
Find the sum to infinity of a geometric series and check convergence, e.g. 1 + 1/2 + 1/4 + … = 2.
Also known as: sum to infinity, infinite sum, convergent series, infinite series calculator.
How to use this calculator
- Enter first term, common ratio.
- The result updates instantly as you type — press Calculate (or Enter) at any time.
- Open “Step-by-step” to see how the answer was worked out.
- Use Copy result or Share to save the answer or send a link with your inputs.
Formula
S∞ = a₁ / (1 − r), valid for |r| < 1
Worked example
Using the values pre-filled in the calculator above:
- First term = 1
- Common ratio = 0.5
the calculator returns:
- Sum to infinity: 2
Working
S∞ = 1 ÷ (1 − 0.5) = 2