mat25-hw9 - Math 25: Advanced Calculus UC Davis, Spring...

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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.

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mat25-hw9 - Math 25: Advanced Calculus UC Davis, Spring...

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