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Infinite Geometric Series Limit Calculator — result sheet
Check convergence and calculate the sum of an infinite geometric series when the absolute ratio is below one.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: If |r|<1, S∞=a₁/(1−r); otherwise the ordinary infinite sum does not converge.
The convergence boundary is the main result: once the ratio’s magnitude reaches one, terms do not approach zero in the required way.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- First term a₁ — minimum -1000000000000; maximum 1000000000000
- Common ratio r — minimum -0.999999; maximum 0.999999
Worked example
| Input | Value |
|---|---|
| First term a₁ | 8 |
| Common ratio r | 0.25 |
Infinite sum ≈10.6667; convergent because |r|<1.
Assumptions and limits
- The series is geometric with a constant ratio.
- The entered ratio is strictly between −1 and 1 for a finite returned sum.
- Other summability methods and complex ratios are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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