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∞ Let Σn(x-9)n be a power series centred at 9. Suppose that the radius of convergence is 5. n=0 Determine the truth of the statement and give a reason for your answer: The Interval of Convergence is (4, 14). False. We need to check if the endpoints are included or not. True. The ratio test says the series is absolutely convergent on this interval. O True. We never include endpoints in the interval of convergence for a power series. False. All power series have both endpoints included in their Interval of Convergence. O False. All power series include only the lower endpoint in their Interval of Convergence.

∞ Let Σn(x-9)n be a power series centred at 9. Suppose that the radius of convergence is 5. n=0 Determine the truth of the statement and give a reason for your answer: The Interval of Convergence is (4, 14). False. We need to check if the endpoints are included or not. True. The ratio test says the series is absolutely convergent on this interval. O True. We never include endpoints in the interval of convergence for a power series. False. All power series have both endpoints included in their Interval of Convergence. O False. All power series include only the lower endpoint in their Interval of Convergence.

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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∞ Let Cn(x-9)n be a power series centred at 9. Suppose that the radius of convergence is 5. n=0 Determine the truth of the statement and give a reason for your answer: The Interval of Convergence is (4, 14). False. We need to check if the endpoints are included or not. True. The ratio test says the series is absolutely convergent on this interval. True. We never include endpoints in the interval of convergence for a power series. False. All power series have both endpoints included in their Interval of Convergence. False. All power series include only the lower endpoint in their Interval of Convergence.
Transcribed Image Text:∞ Let Cn(x-9)n be a power series centred at 9. Suppose that the radius of convergence is 5. n=0 Determine the truth of the statement and give a reason for your answer: The Interval of Convergence is (4, 14). False. We need to check if the endpoints are included or not. True. The ratio test says the series is absolutely convergent on this interval. True. We never include endpoints in the interval of convergence for a power series. False. All power series have both endpoints included in their Interval of Convergence. False. All power series include only the lower endpoint in their Interval of Convergence.
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