Geometric Series Calculator
Calculate the sum of a geometric series given the first term, common ratio, and number of terms.
Also shows infinite sum when |r| < 1.
Series Sum
Geometric series is a sequence where each term is multiplied by a constant ratio.
Finite sum (n terms):
S = a × (1 − rⁿ) / (1 − r) when r ≠ 1, or S = a × n when r = 1
Where:
- a = first term
- r = common ratio
- n = number of terms
Infinite sum (only converges when |r| < 1):
S∞ = a / (1 − r)
Examples:
- a=1, r=0.5: 1, 0.5, 0.25, 0.125… → S∞ = 2
- a=3, r=2, n=5: 3, 6, 12, 24, 48 → S = 93