MathLiveRatio test
The ratio test checks the limit of the ratio of consecutive terms of an infinite series. If that ratio is at most some number q below 1 for all large n, the series converges absolutely. If the limit of the ratio exceeds 1, the series diverges; if the limit equals 1, the test is inconclusive.
\left|\frac{a_{n+1}}{a_n}\right|\leq q<1What the symbols mean
| the n-th term of the series | |
| the next term of the series, after a_n | |
| a fixed constant strictly less than 1 bounding the ratio of consecutive terms for large n |
About this formula
- FieldMathematics
- TopicConvergence tests
- LevelUniversity
- Also calledd'Alembert's ratio test, Cauchy ratio test, d'Alembert's criterion, series convergence ratio test, test for convergence of series, ratio test for series convergence
- SourceWikidata Q165638
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