Ratio and Root Tests — Cheat sheet
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Core rule
Ratio or root limit: gives absolute convergence; gives divergence; is inconclusive.
Watch for
Use absolute values. A test that is inconclusive is not a proof of divergence.
Mr. IntegralMr. IntegralRatio or root limit: gives absolute convergence; gives divergence; is inconclusive.
Use absolute values. A test that is inconclusive is not a proof of divergence.