Sequences and series
Sequences: explicit and recursive formulas, Arithmetic sequences, Geometric sequences, Sigma notation and arithmetic series, Finite geometric series, The binomial theorem, Infinite geometric series, Convergence of series; the nth-term test, The integral test and p-series, Comparison tests, Alternating series and the error bound, The ratio test; absolute and conditional convergence, Choosing a convergence test, Taylor polynomials, The Lagrange error bound, Radius and interval of convergence of a power series, Maclaurin series of eˣ, sin x, cos x and 1/(1 − x), New series from known ones
Arithmetic and geometric sequences, series, the binomial theorem
Practice
Lessons, in order
- 1. Sequences: explicit and recursive formulas
- 2. Arithmetic sequences
- 3. Geometric sequences
- 4. Sigma notation and arithmetic series
- 5. Finite geometric series
- 6. The binomial theorem
- 7. Infinite geometric series
- 8. Convergence of series; the nth-term test
- 9. The integral test and p-series
- 10. Comparison tests
- 11. Alternating series and the error bound
- 12. The ratio test; absolute and conditional convergence
- 13. Choosing a convergence test
- 14. Taylor polynomials
- 15. The Lagrange error bound
- 16. Radius and interval of convergence of a power series
- 17. Maclaurin series of eˣ, sin x, cos x and 1/(1 − x)
- 18. New series from known ones