Calculatrice de Somme de Série Géométrique Gratuite
Calculez la somme d'une série géométrique finie ou infinie. Trouvez la somme des termes d'une progression géométrique.
Finite Sum
1.998047
Last Term0.001953
Formule
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.
Exemple Résolu
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
Questions Fréquentes
When does a geometric series converge?
A geometric series converges (has a finite sum) only when the absolute value of the common ratio is less than 1 (|r| < 1).
What is the classic example of a convergent geometric series?
1 + 1/2 + 1/4 + 1/8 + ... converges to 2. This can be visualized by repeatedly halving the remaining distance to 2.
What happens when r = 1?
When r = 1, every term equals a, so the sum of n terms is simply n × a. The infinite sum diverges.
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