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10. Determine whether the following p-series are convergent or divergent. J tify your answer. (a) MAT n=₁ n³ ê n=1 iM8 4 (0)2 +/ TL=

10. Determine whether the following p-series are convergent or divergent. J tify your answer. (a) MAT n=₁ n³ ê n=1 iM8 4 (0)2 +/ TL=

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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Solve 10 a determine whether the following p series are convergent or divergent
**Educational Content on Series Convergence Tests** **Page 2** **Problem 9: Divergence Test** - Use the divergence test to determine whether the series is convergent or divergent. Justify your answer. Turn in at least two problems. (a) \(\sum_{n=1}^{\infty} \frac{n^2 + 3n - 1}{4n^2 + 5n + 3}\) **Problem 10: p-Series Convergence** - Determine whether the following p-series are convergent or divergent. Justify your answer. (a) \(\sum_{n=1}^{\infty} \frac{1}{n^{2/3}}\) (b) \(\sum_{n=1}^{\infty} \frac{2}{n^{3/2}}\) **Problem 11: Integral Test** - Use the integral test to determine whether the series is convergent or divergent. Make sure to check the assumptions of the test first. Justify your answer. Turn in at least two problems. (a) \(\sum_{n=1}^{\infty} \frac{2}{4n + 5}\) (b) \(\sum_{n=1}^{\infty} \frac{1}{(3n - 1)^4}\) (c) \(\sum_{n=1}^{\infty} \frac{3}{4\sqrt{n}}\) Remember to fully explain your reasoning and steps taken in determining the convergence or divergence of each series.
Transcribed Image Text:**Educational Content on Series Convergence Tests** **Page 2** **Problem 9: Divergence Test** - Use the divergence test to determine whether the series is convergent or divergent. Justify your answer. Turn in at least two problems. (a) \(\sum_{n=1}^{\infty} \frac{n^2 + 3n - 1}{4n^2 + 5n + 3}\) **Problem 10: p-Series Convergence** - Determine whether the following p-series are convergent or divergent. Justify your answer. (a) \(\sum_{n=1}^{\infty} \frac{1}{n^{2/3}}\) (b) \(\sum_{n=1}^{\infty} \frac{2}{n^{3/2}}\) **Problem 11: Integral Test** - Use the integral test to determine whether the series is convergent or divergent. Make sure to check the assumptions of the test first. Justify your answer. Turn in at least two problems. (a) \(\sum_{n=1}^{\infty} \frac{2}{4n + 5}\) (b) \(\sum_{n=1}^{\infty} \frac{1}{(3n - 1)^4}\) (c) \(\sum_{n=1}^{\infty} \frac{3}{4\sqrt{n}}\) Remember to fully explain your reasoning and steps taken in determining the convergence or divergence of each series.
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