How to use the infinite geometric series sum calculator
Find the sum of an infinite geometric series when the common ratio is between -1 and 1. Enter first term, common ratio in the fields above; the sum to infinity, convergence check are computed instantly and plotted on the chart so you can see how the answer changes.
Common searches this calculator answers include “infinite geometric series sum”, “a over 1 minus r”, “convergent geometric series”, “calculate infinite geometric series sum”, “find sum to infinity”.
Formula
Variables
- a — First term
- r — Common ratio
Worked example
With first term = 1, common ratio = 0.5, the calculator gives sum to infinity ≈ 2; convergence check ≈ Converges text.
Frequently asked questions
What is the infinite geometric series sum calculator used for?
Find the sum of an infinite geometric series when the common ratio is between -1 and 1. It helps with questions such as “infinite geometric series sum”, “a over 1 minus r”, “convergent geometric series”.
What is the formula for the infinite geometric series sum calculation?
Sum to infinity = a / (1-r). Convergence check (text) = abs(r)<1?"Converges":"Diverges". Here a is first term, r is common ratio.
What inputs do I need for the infinite geometric series sum calculator?
You need first term, common ratio. Each field is pre-filled with a typical example so you can see how the result responds as you edit the numbers.
How do I use the infinite geometric series sum calculator?
Type values into the input fields. Results and the chart update instantly. Use Reset to restore the example values, Copy results to paste them elsewhere, or Share to copy a link that preserves your inputs.
Is the infinite geometric series sum result exact?
Calculations use standard formulas and double-precision arithmetic, then display about seven significant figures. Real-world measurements carry uncertainty, so treat results as estimates unless your inputs are exact.