Section You should be able to … Example Review Exercises
8.1 1 Write the terms of a sequence (p. 539) 1,2 1, 2
2 Find the \(n\)th term of a sequence (p. 539) 3, 4 3
3 Use properties of convergent sequences (p. 542) 5, 6 4, 5
4 Use a related function or the Squeeze Theorem to show a sequence converges (p. 543) 7–10 6, 7
5 Determine whether a sequence converges or diverges (p. 545) 11–15 8–13
8.2 1 Determine whether a series has a sum (p. 554) 1–3 14, 15
2 Analyze a geometric series (p. 557) 4–6 17–20
3 Analyze the harmonic series (p. 561) 16
8.3 1 Use the Test for Divergence (p. 567) 1 21
2 Work with properties of series (p. 567) 2 25–27
3 Use the Integral Test (p. 569) 3–5 22, 23
4 Analyze a \(p\)-series (p. 570) 6 24
8.4 1 Use Comparison Tests for Convergence and Divergence (p. 576) 1, 2 28
2 Use the Limit Comparison Test (p. 577) 3, 4 28–30
8.5 1 Determine whether an alternating series converges (p. 583) 1, 2 31–33
2 Approximate the sum of a convergent alternating series (p. 584) 3 31–33
3 Determine whether a series converges (p. 586) 4–6 34–37
8.6 1 Use the Ratio Test (p. 591) 1,2 38, 39
2 Use the Root Test (p. 593) 3,4 40, 41
8.7 1 Choose an appropriate test to determine whether a series converges (p. 596) 42–52
8.8 1 Determine whether a power series converges (p. 600) 1 53(a)–58(a)
2 Find the interval of convergence of a power series (p. 603) 2–4 53(b)–58(b)
3 Define a function using a power series (p. 604) 5,6 59, 60
4 Use properties of power series (p. 606) 7–9 61
8.9 1 Express a function as a Taylor series or a Maclaurin series (p. 613) 1 64
2 Determine the convergence of a Taylor/Maclaurin series (p. 614) 2
3 Find Taylor/Maclaurin expansions (p. 616) 3–7 62, 63, 65, 66
4 Work with a binomial series (p. 619) 8–10 67–69
8.10 1 Approximate functions and their graphs (p. 623) 1, 2 70
2 Approximate the number \(e;\) approximate logarithms (p. 625) 3, 4 71
3 Approximate definite integrals (p. 627) 5 72, 73