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Ratio Test for Series — result sheet
Judge absolute convergence from consecutive-term ratios.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: r = |a(n+1)/a(n)|; r < 1 converges, r > 1 diverges, r = 1 inconclusive.
Ratios below 1 signal geometric-like decay; above 1 signal growth. A ratio of exactly 1 (within 1e-12) decides nothing.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Sequence terms — At least 2 nonzero terms in order.
Worked example
| Input | Value |
|---|---|
| Sequence terms | 1, 0.5, 0.25, 0.125 |
Last ratio 0.5: converges absolutely.
Assumptions and limits
- Terms in order, at least 2, all nonzero and finite.
- Verdict uses the last ratio as the limit proxy.
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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