等比级数求和计算器 — 公式
## Geometric Series Sum
### Finite Sum
**Sₙ = a × (1 - r^n) / (1 - r)** (when r ≠ 1)
### Infinite Sum (converges only when |r| < 1)
**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.
### Finite Sum
**Sₙ = a × (1 - r^n) / (1 - r)** (when r ≠ 1)
### Infinite Sum (converges only when |r| < 1)
**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.
计算示例
1 + 0.5 + 0.25 + 0.125 + ... (10 terms and infinite).
- Finite sum (10 terms) = 1 × (1 - 0.5¹⁰)/(1 - 0.5) = (1 - 0.000977)/0.5 ≈ 1.998047
- Infinite sum = 1/(1-0.5) = 2
- Last term = 1 × 0.5⁹ = 0.001953