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Material Type: Notes; Professor: Ledyaev; Class: Advanced Calculus II; Subject: Mathematics; University: Western Michigan University; Term: Spring 2009;
Typology: Study notes
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Definition of a sum of an infinite series ( Definition 34.1). Properties of convergent series (Theorem 34.1). Convergence of an infinite series with positive terms (Theorem 36.4). Cauchy criteria for convergence of series (Theorem 34.5). Definition 34.6 of absolutely convergent and conditionally convergent series. Tests for absolute convergence: Comparison test (Theorem 35.1), Limit comparison test (Theorem 35.2), Root test (Theorem 35.3) and Ratio test (Theorem 35.6), Integral test (Theorem 35.12). Conditional convergence of series: Abel lemma (Theorem 36.1), Dirichlet test (The- orem 36.2). Alternating series : Definition 36.6 and Test (Theorem 36.7).
Homework problems: Section 34: B, F, G, H, O. Section 35 : A (b)-(g), B, C (b)-(e)
Quiz problems - examples.
n + 3)(n + 2)^2
(b) xn = n!/nn
(c) xn = (−1)nn/(n + 1)
(d) xn = 2ne−n
(e) xn = n!e−n 2
∑^ ∞
n=
(−1)n n + np