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 30, 31, 32 · 7 college lessons
Sequences & Infinite Series Foundations
How do sequence behavior, partial sums, comparison models, and remainder estimates determine whether infinite accumulation has a finite value?
Pathways
Lesson 01 · Week 30
Sequence Limits & Long-Run Behavior
Evaluating indexed limits with algebra and dominant terms.
Lesson 02 · Week 30Monotone, Bounded & Recursive Sequences
Using structural properties to prove convergence.
Lesson 03 · Week 30Infinite Series & Partial-Sum Sequences
Defining a series through the limit of partial sums.
Lesson 04 · Week 31Geometric & Telescoping Series
Recognizing exact sum structures.
Lesson 05 · Week 31The nth-Term Divergence Test
Using the necessary condition a_n→0.
Lesson 06 · Week 32Integral Test, p-Series & Continuous Comparison
Connecting decreasing positive terms to improper integrals.
Lesson 07 · Week 32Integral-Test Remainders & Approximation
Bounding the tail after a finite partial sum.