KnowraRoot testLinked fromLinked fromThe 10 pages that link to Root test, each with the reason it gives.All 10Related 4Compared with 6Absolute convergenceRelated: It identifies absolute convergence when the nth-root limit is below one.Radius of convergenceRelated: It gives a radius formula directly from the coefficients, including when ratios fail.Ratio testCompared with: It often reaches the same conclusion as the ratio test, but can work when successive ratios do not settle.Alternating series testCompared with: It analyzes term magnitudes directly rather than relying on alternating signs.Comparison testCompared with: It is an alternative for terms raised to the nth power.Convergent seriesRelated: It detects convergence when terms have a persistent exponential scale.Cauchy condensation testCompared with: It detects exponential-scale decay directly rather than grouping terms by powers of two.Cauchy–Hadamard theoremRelated: Applied to power-series terms, it yields the theorem’s radius formula.Integral test for convergenceCompared with: It can detect exponential behavior without requiring monotonicity of a related function.Nth-term testCompared with: It extracts exponential decay information that the term limit alone misses.