SalasSV_11_highlights

SalasSV_11_highlights - CHAPTER HIGHLIGHTS 703 CHAPTER...

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Unformatted text preview: CHAPTER HIGHLIGHTS 703 CHAPTER HIGHLIGHTS 11.1 Infinite Series sigma notation (p. 633) partial sums (p. 634) convergence, divergence (p. 635) sum of a series(p. 635) a divergence test (p. 641) geometric series: k = x k = ( 1 1 x , | x | < 1 diverges, | x | 1 If k = a k converges, then a k 0. The converse is false. 11.2 The integral Test; Comparison Tests integral test (p. 644) basic comparison (p. 647) limit comparison (p. 649) harmonic series: k = 1 1 k diverges p-series: k = 1 1 k p converges iff p > 1 11.3 The Root Test; The Ratio Test root test (p. 653) ratio test (p. 654) summary on convergence tests (p. 656) 11.4 Absolute and Conditional Convergence; Alternating Series absolutely convergent, conditionally convergent (p. 657) convergence theorem for alternating series (p.659) an estimate for alternating series (p.660) rearrangements (p.662) 11.5 Taylor Polynomials in x ; Taylor Series in x Taylor polynomials in x (p. 665) remainder term R n (...
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