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Series-Overviewr - alternating series test(page 710(d a n...

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Series - Overview Series n =1 a n Main Question: estimate value to which it converges % Converge? find exact value to which it converges Diverge? Tests: (a) Test for divergence: (page 692) if a n 6→ 0 as n → ∞ then series diverges (b) a n 0: geometric series (page 689) telescoping series (page 691) integral test (page 699) comparison test (page 705) limit comparison test (page 707) (c) a n is alternating in sign:
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Unformatted text preview: alternating series test (page 710) (d) a n is any real number absolute convergence (page 714-715) ratio test (page 716) root test (page 718) • Functions defined by series: (a) functions defined as power series (section 11.8) (b) Representing functions as power series, Taylor and Maclaurin series (sections 11.9, 11.10) 1...
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