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Unformatted text preview: Math 25: Advanced Calculus UC Davis, Spring 2011 Math 25 — Homework Assignment #9 Homework due: Tuesday 5/31/11 at beginning of discussion section Reading material. Read section 3.4, 3.5, 3.6.1, 3.6.2, 3.6.12 in the text book. Problems 1. Decide whether or not each of the following infinite series converges or diverges. Prove your claims. (a) ∞ X n =1 1 n √ n (d) ∞ X n =1 3 n ( n + 1)( n + 2) n 3 √ n (b) ∞ X n =1 1 n n (e) ∞ X n =1 n + 2 ( n 2 + 1) √ n (c) ∞ X n =1 n ( n + 1) ( n + 2) 2 (f) ∞ X n =2 ( 1) n ln( n ) 2. Find the value of the ( hint: telescoping) infinite sum ∞ X n =1 1 n ( n + 1)( n + 2) = 1 1 · 2 · 3 + 1 2 · 3 · 4 + 1 3 · 4 · 5 + 1 4 · 5 · 6 + ... 3. If ( a n ) ∞ n =1 ( b n ) ∞ n =1 are sequences such that a n ,b n ≥ 0 for all n ≥ 1, and the sums ∑ ∞ n =1 a n and ∑ ∞ n =1 b n are convergent, prove that ∑ ∞ n =1 a n b n converges as well....
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This note was uploaded on 10/16/2011 for the course MATH 34 taught by Professor Wiley during the Winter '11 term at UC Merced.
 Winter '11
 Wiley
 Differential Equations, Calculus, Equations

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