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gence divergence of the series. 14. 13. У n+1 4 + 1 2n + 16. 15. Y 5 +1 0 Vn- +1 2n2 - 1 1 18. 17. 3n + 2n + 1 n2(n + 3) 80

gence divergence of the series. 14. 13. У n+1 4 + 1 2n + 16. 15. Y 5 +1 0 Vn- +1 2n2 - 1 1 18. 17. 3n + 2n + 1 n2(n + 3) 80

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Series Convergence and Divergence Exercises** **Using the Direct Comparison Test** Determine the convergence or divergence of the following series: 1. \(\sum_{n=1}^{\infty} \frac{1}{n^3}\) 2. \(\sum_{n=1}^{\infty} \frac{1}{3^n}\) 3. \(\sum_{n=1}^{\infty} \frac{2^n}{n!}\) 4. \(\sum_{n=1}^{\infty} \frac{3n}{n^2 + 1}\) 5. \(\sum_{n=1}^{\infty} \frac{5}{n^2 + 2}\) 6. \(\sum_{n=1}^{\infty} \frac{1}{n \sqrt{n}}\) 7. \(\sum_{n=1}^{\infty} \frac{1}{n^5}\) 8. \(\sum_{n=1}^{\infty} \frac{1}{n \cdot 3^n}\) 9. \(\sum_{n=1}^{\infty} \frac{2^n}{3^n}\) 10. \(\sum_{n=1}^{\infty} \frac{3^n}{4^n}\) 11. \(\sum_{n=1}^{\infty} \frac{e^n}{4^n}\) 12. \(\sum_{n=1}^{\infty} \frac{4^n}{5^n}\) **Using the Limit Comparison Test** Determine the convergence or divergence of the following series: 13. \(\sum_{n=1}^{\infty} \frac{n}{n^2 + 1}\) 14. \(\sum_{n=1}^{\infty} \frac{5}{2^n + 1}\) 15. \(\sum_{n=1}^{\infty} \frac{2n^2 - 1}{3n^5 + 2n + 1}\) 16. \(\sum_{n=1}^{\infty} \frac{1}{5^n + 1}\) 17. \(\sum_{n=1}^{\infty} \frac{1}{n \cdot ((n+3
Transcribed Image Text:**Series Convergence and Divergence Exercises** **Using the Direct Comparison Test** Determine the convergence or divergence of the following series: 1. \(\sum_{n=1}^{\infty} \frac{1}{n^3}\) 2. \(\sum_{n=1}^{\infty} \frac{1}{3^n}\) 3. \(\sum_{n=1}^{\infty} \frac{2^n}{n!}\) 4. \(\sum_{n=1}^{\infty} \frac{3n}{n^2 + 1}\) 5. \(\sum_{n=1}^{\infty} \frac{5}{n^2 + 2}\) 6. \(\sum_{n=1}^{\infty} \frac{1}{n \sqrt{n}}\) 7. \(\sum_{n=1}^{\infty} \frac{1}{n^5}\) 8. \(\sum_{n=1}^{\infty} \frac{1}{n \cdot 3^n}\) 9. \(\sum_{n=1}^{\infty} \frac{2^n}{3^n}\) 10. \(\sum_{n=1}^{\infty} \frac{3^n}{4^n}\) 11. \(\sum_{n=1}^{\infty} \frac{e^n}{4^n}\) 12. \(\sum_{n=1}^{\infty} \frac{4^n}{5^n}\) **Using the Limit Comparison Test** Determine the convergence or divergence of the following series: 13. \(\sum_{n=1}^{\infty} \frac{n}{n^2 + 1}\) 14. \(\sum_{n=1}^{\infty} \frac{5}{2^n + 1}\) 15. \(\sum_{n=1}^{\infty} \frac{2n^2 - 1}{3n^5 + 2n + 1}\) 16. \(\sum_{n=1}^{\infty} \frac{1}{5^n + 1}\) 17. \(\sum_{n=1}^{\infty} \frac{1}{n \cdot ((n+3
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