Unit 10 — Weeks 22–23: convergence tests
- Sequence convergence/divergence; partial sums intro; partial sums & series: nth-term from partials; infinite geometric series a/(1−r); quiz
- nth-term (divergence) test; integral test for convergence; p-series + harmonic series; direct comparison test
- Limit comparison test; alternating series test; ratio test; absolute vs conditional convergence; quiz
- Test-selection flowchart drill: 20 series, name the test only, 30 min. Note: ratio = 1 is inconclusive — must state it
Unit 10 — Weeks 24–25: Taylor + error + interval
- Alternating series remainder |Rₙ|≤bₙ₊₁; Taylor & Maclaurin polynomials intro + worked Maclaurin/coefficient examples; visualizing approximations
- Lagrange error bound: remainder + worked sin(0.4) and eˣ estimates; radius/interval of convergence: power-series intro + worked interval example
- Function as geometric series (substitution); Maclaurin series of sin, cos, eˣ; differentiate + integrate power series term-by-term; integrals/derivatives of known series; quiz + unit test
- TIMED SERIES FRQ weekly: 2023 BC #6, 2022 BC #6, 2024 BC #6 — grade with official rubric, require test-name + setup lines
Decision tree: nth-term → geometric/p-series? → alternating? → ratio (!/ⁿ) → integral/comparison. CED: LIM-7–LIM-8.