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Which of the following series converge? (i) Σn=1_n²+2 2n² +∞ (ii) Σ in= (ii)Σ+3# O (i) and (iii) only (ii) and (iii) only O (i) and (ii) only ++ (1) 2 1+ 3 All of the above series converge. None of the above series converge.

Which of the following series converge? (i) Σn=1_n²+2 2n² +∞ (ii) Σ in= (ii)Σ+3# O (i) and (iii) only (ii) and (iii) only O (i) and (ii) only ++ (1) 2 1+ 3 All of the above series converge. None of the above series converge.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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### Convergence of Series Consider the following series and determine which of them converge: 1. \( \text{(i)} \quad \sum_{n=1}^{\infty} \frac{2n^2}{n^2 + 2} \) 2. \( \text{(ii)} \quad \sum_{n=1}^{\infty} \frac{1}{1 + \left( \frac{2}{3} \right)^n} \) 3. \( \text{(iii)} \quad \sum_{n=1}^{\infty} 3^{\frac{1}{n}} \) ### Multiple Choice Options - \( \quad \circ \quad \text{(i) and (iii) only} \) - \( \quad \circ \quad \text{(ii) and (iii) only} \) - \( \quad \circ \quad \text{(i) and (ii) only} \) - \( \quad \circ \quad \text{All of the above series converge.} \) - \( \quad \bullet \quad \text{None of the above series converge.} \) The solution to the convergence question has been identified. The correct answer is: - \( \quad \bullet \quad \text{None of the above series converge.} \)
Transcribed Image Text:### Convergence of Series Consider the following series and determine which of them converge: 1. \( \text{(i)} \quad \sum_{n=1}^{\infty} \frac{2n^2}{n^2 + 2} \) 2. \( \text{(ii)} \quad \sum_{n=1}^{\infty} \frac{1}{1 + \left( \frac{2}{3} \right)^n} \) 3. \( \text{(iii)} \quad \sum_{n=1}^{\infty} 3^{\frac{1}{n}} \) ### Multiple Choice Options - \( \quad \circ \quad \text{(i) and (iii) only} \) - \( \quad \circ \quad \text{(ii) and (iii) only} \) - \( \quad \circ \quad \text{(i) and (ii) only} \) - \( \quad \circ \quad \text{All of the above series converge.} \) - \( \quad \bullet \quad \text{None of the above series converge.} \) The solution to the convergence question has been identified. The correct answer is: - \( \quad \bullet \quad \text{None of the above series converge.} \)
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