5. 6. IM8 IM8 IM8 8n5 Σ nϑ +7 n=1 n=1 7. Σ 4n? – n + 8vn 7nl1 – n5 + 3 cos² (n) √n n5
5. 6. IM8 IM8 IM8 8n5 Σ nϑ +7 n=1 n=1 7. Σ 4n? – n + 8vn 7nl1 – n5 + 3 cos² (n) √n n5
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
5-7) For each of the series, test for convergence using either the limit comparison test and comparison test. If one of the tests apply, decide if it either converges, diverges or neither test applies:
![### Mathematical Series
**5. Series Expression**
\[ \sum_{n=1}^{\infty} \frac{8n^5}{n^9 + 7} \]
This represents an infinite series where each term is given by the expression \( \frac{8n^5}{n^9 + 7} \).
**6. Series Expression**
\[ \sum_{n=1}^{\infty} \frac{4n^9 - n^6 + 8\sqrt{n}}{7n^{11} - n^5 + 3} \]
This is another infinite series with terms expressed as \( \frac{4n^9 - n^6 + 8\sqrt{n}}{7n^{11} - n^5 + 3} \).
**7. Series Expression**
\[ \sum_{n=1}^{\infty} \frac{\cos^2(n)\sqrt{n}}{n^5} \]
This series involves the cosine function and is defined by the expression \( \frac{\cos^2(n)\sqrt{n}}{n^5} \) for each term.
These mathematical series are useful in various fields, including calculus and mathematical analysis, for understanding convergence and the behavior of functions as \( n \) approaches infinity.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb96d91a2-1904-4455-9ca0-61adba14ab53%2F7a8289b7-2786-4358-b27f-a5b45a4a924e%2Fm28qzqa_processed.png&w=3840&q=75)
Transcribed Image Text:### Mathematical Series
**5. Series Expression**
\[ \sum_{n=1}^{\infty} \frac{8n^5}{n^9 + 7} \]
This represents an infinite series where each term is given by the expression \( \frac{8n^5}{n^9 + 7} \).
**6. Series Expression**
\[ \sum_{n=1}^{\infty} \frac{4n^9 - n^6 + 8\sqrt{n}}{7n^{11} - n^5 + 3} \]
This is another infinite series with terms expressed as \( \frac{4n^9 - n^6 + 8\sqrt{n}}{7n^{11} - n^5 + 3} \).
**7. Series Expression**
\[ \sum_{n=1}^{\infty} \frac{\cos^2(n)\sqrt{n}}{n^5} \]
This series involves the cosine function and is defined by the expression \( \frac{\cos^2(n)\sqrt{n}}{n^5} \) for each term.
These mathematical series are useful in various fields, including calculus and mathematical analysis, for understanding convergence and the behavior of functions as \( n \) approaches infinity.
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