Convergence Tests Flowchart and Visual Guide
An accessible decision guide for selecting a convergence test without replacing the proof.
Reference format20 min estimated timeReference progression
What is included
Compare nth-term, geometric, p-series, comparison, integral, alternating, ratio, and root tests with cautions.
Skills assessed
- test selection
- hypothesis checks
- absolute versus conditional convergence
Prerequisites
- sequences
- series
- improper integrals
Long description
Read the diagram from top to bottom. Each numbered box names one decision or mathematical operation. Arrows show the required order; the text labels remain the complete interpretation in print, dark mode, and nonvisual reading.
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Common errors
- Using the nth-term test to prove convergence.
- Applying comparison tests without nonnegative terms.
- Treating a ratio-test limit of one as a conclusion.