Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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## Series Convergence Questions ### Question 1: Does the series \(\sum_{k=1}^{\infty} \frac{1}{\sqrt[3]{k^4 + 8}}\) converge absolutely, converge conditionally, or diverge? - ○ converges absolutely - ○ converges conditionally - ○ diverges ### Question 2: Does the series \(\sum_{k=1}^{\infty} \frac{(-1)^k}{\sqrt[3]{k^4 + 8}}\) converge absolutely, converge conditionally, or diverge? - ○ converges absolutely - ○ converges conditionally - ○ diverges Each question requires determining the type of convergence or divergence for the provided series. Analyze the series by applying relevant convergence tests, such as the comparison test, ratio test, or alternating series test, to determine the correct choice.
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Transcribed Image Text:## Series Convergence Questions ### Question 1: Does the series \(\sum_{k=1}^{\infty} \frac{1}{\sqrt[3]{k^4 + 8}}\) converge absolutely, converge conditionally, or diverge? - ○ converges absolutely - ○ converges conditionally - ○ diverges ### Question 2: Does the series \(\sum_{k=1}^{\infty} \frac{(-1)^k}{\sqrt[3]{k^4 + 8}}\) converge absolutely, converge conditionally, or diverge? - ○ converges absolutely - ○ converges conditionally - ○ diverges Each question requires determining the type of convergence or divergence for the provided series. Analyze the series by applying relevant convergence tests, such as the comparison test, ratio test, or alternating series test, to determine the correct choice.
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