Calculadora de Suma de Series Geométricas
Calcula la suma de los primeros n términos de una serie geométrica. Introduce el primer término, la razón común y la cantidad de términos.
Finite Sum
1.998047
Fórmula
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.
Ejemplo Resuelto
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
Preguntas Frecuentes
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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