Geometric Series Calculator

Calculate the sum of geometric series with step-by-step solutions. Find finite and infinite sums.

Series Parameters

First Term (a)

Common Ratio (r)

Number of Terms (n)

General Term:

a_n = 2 × 0.5^(n-1)

Sum of First 10 Terms

3.996094

S_10 = 2 × (1 - 0.5^10) / (1 - 0.5)

Infinite Sum (|r| < 1)

4.000000

S_∞ = 2 / (1 - 0.5)

nth Term: a_10

0.003906

First Terms

2.00001.00000.50000.25000.12500.06250.03130.01560.00780.0039

Partial Sums

S_12.0000

S_23.0000

S_33.5000

S_43.7500

S_53.8750

S_63.9375

S_73.9688

S_83.9844

S_93.9922

S_103.9961

Finite Sum (r ≠ 1)

S_n = a(1 - r^n) / (1 - r)

S_n = a(r^n - 1) / (r - 1)

Infinite Sum (|r| < 1)

S_∞ = a / (1 - r)

Only converges when |r| < 1

Sequence terms

Arithmetic sequences