Geometric Series Sum Calculator
Calculate the finite and infinite sum of a geometric series.
Finite Sum
1.998047
Last Term0.001953
Geometric Series Sum
Finite Sum
Sₙ = a × (1 - r^n) / (1 - r) (when r ≠ 1)
Infinite Sum (converges only when r
S∞ = a / (1 - r)
Example
1 + 1/2 + 1/4 + 1/8 + ... = 1 / (1 - 0.5) = 2
The infinite sum converges to a finite value when the common ratio has absolute value less than 1.
Example Calculation
1 + 0.5 + 0.25 + 0.125 + ... (10 terms and infinite).
- 01Finite sum (10 terms) = 1 × (1 - 0.5¹⁰)/(1 - 0.5) = (1 - 0.000977)/0.5 ≈ 1.998047
- 02Infinite sum = 1/(1-0.5) = 2
- 03Last term = 1 × 0.5⁹ = 0.001953
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