How this calculation works
The closer the ratio is to magnitude one, the more terms it takes for partial sums to approach the limit.
THE FORMULA
S = a/(1−r) when |r| < 1A worked example
12 + 3 + 0.75 + … sums to 16.
Good to know
A nonzero geometric series converges only for |r| < 1.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Find the limiting total of a convergent geometric series.
The primary result is labeled “Infinite sum”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
A nonzero geometric series converges only for |r| < 1.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
12 + 3 + 0.75 + … sums to 16.
Which rule does this calculator apply?
S = a/(1−r) when |r| < 1