Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 33, 34 · 7 college lessons
Convergence Tests & Conditional Behavior
How can comparison, alternation, ratios, roots, and absolute convergence classify series and quantify approximation reliability?
Pathways
Lesson 01 · Week 33
Direct Comparison Test
Building inequalities against known benchmark series.
Lesson 02 · Week 33Limit Comparison Test
Comparing asymptotic size when direct inequalities are awkward.
Lesson 03 · Week 33Alternating Series & Error Bounds
Using decreasing magnitudes and a zero limit.
Lesson 04 · Week 33Absolute vs Conditional Convergence
Distinguishing convergence of σa_n from σ|a_n|.
Lesson 05 · Week 34Ratio Test
Measuring factorial and exponential growth.
Lesson 06 · Week 34Root Test
Measuring nth-power growth.
Lesson 07 · Week 34Test Selection, Counterexamples & Decision Logic
Selecting a test from structure and explaining inconclusive outcomes.