Geometric Series Sum Calculator
Sum of a finite or infinite geometric series.
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ⓘ Live results
Results
- Finite sum (n terms)
- 3.984375
- Infinite sum
- 4
- Common ratio
- 0.5
Quick answer
A finite geometric series sums to a(1-r^n)/(1-r); an infinite series only converges to a/(1-r) when |r|<1.
S_n = a(1-r^n)/(1-r)
How to use the Geometric Series Sum Calculator
- 1Enter the first term and the common ratio between terms.
- 2Enter how many terms to sum for the finite sum.
- 3If |r|<1, the infinite sum is also shown since the series converges.
Worked example
Using the values the calculator loads with:
Inputs
- First term a12
- Common ratio r0.5
- Number of terms n8
Results
- Finite sum (n terms)3.984375
- Infinite sum4
- Common ratio0.5
Frequently asked questions
When does an infinite geometric series converge?
Only when the absolute value of the common ratio is less than 1.
What if r = 1?
Every term is the same, so the sum is just a times n.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.