// multi-utility computation suite · offline · instant · precise
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math.geometric-series Calculator
Calculates finite and infinite geometric series sums from the first term and common ratio, and checks convergence condition |r| < 1. The infinite geometric series sum (a/(1−r)) is the formula behind the present value of a perpetuity in finance.
Inputs
A
Reference formula or conversion factor shown for context.
R
Reference formula or conversion factor shown for context.
N
Count of items or occurrences.
Results
finite sum (n terms)
The arithmetic total of all input values.
infinite sum
The arithmetic total of all input values.
nth term
Sample size or count used in the calculation.
ratio r
The proportional relationship between two quantities.
converges?
Sample size or count used in the calculation.
S = a/(1-r) for |r|<1
Reference formula or conversion factor shown for context.