Theory Stuff for Chapter 8

Note: You may use the table on page 593 on my quizzes, but not on the final.

Section 8.1
Know the definitions of convergence and divergence for sequences. Be able to prove convergence or divergence for simple cases from the definitions.
Theorem 8.1: This is a obvious.
Theorem 8.2: (Properties of Limits of Sequences) Know these. Be able to prove 1 and 2.
Theorem 8.3: (Squeeze Theorem) Understand proof intuitively.
Theorem 8.4: This is a obvious.
Know definitions of bounded and monotone sequences.
Theorem 8.5: (Bounded Monotone Converge) Important to know. Understand proof intuitively.
Section 8.2
Know the definitions of convergence and divergence for series.
Know definition of telescoping series, page 559.
Theorem 8.6: (Geometric Series) Important. Know how to prove.
Theorem 8.7: (Properties of Infinite Series) Know these. Know how to prove them.
Theorems 8.8 & 8.9: (n-th term test) Know how to prove.
Section 8.3
Theorem 8.10: (Integral Test) Understand proof intuitively.
Theorem 8.11: (p-series Test) Know how to prove.
Section 8.4
Theorem 8.12: (Direct Comparison Test) Understand proof intuitively.
Theorem 8.13: (Limit Comparison Test) Know how to use.
Section 8.5
Theorem 8.14: (Alternating Series Test) Understand proof intuitively.
Theorem 8.15: (Alternating Series Remainder) Know how to use.
Know definitions of absolute and conditional convergence.
Theorem 8.16: (Absolute Convergence Tests) Know how to use.
Section 8.6
Theorem 8.17: (Ratio Test) Know how to use.
Theorem 8.18: (Root Test) Know how to use.
Section 8.7
Know definition of Taylor Polynomial.
Theorem 8.19: Understand statement of. Know how to use.
Section 8.8
Know Definition of power series.
Theorem 8.20: Know how to use.
Theorem 8.21: Know how to use.
Section 8.9
Theorem 8.22: Know how to use.
Section 8.10
Theorem 8.23: Understand statement of.
Know definition of Taylor series (as opposed to Taylor polynomials)