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2. Consider the power series > ar(x + 2)*. Assume that we know that the series > ak converges, but that k=0 k=0 Ear(1*) diverges. k=0 (a) Does the power series converge at x = -1.3? Explain how you know, or explain why you don't have enough information to answer the question. (b) Does the series > ak(5)* converge or diverge? Explain how you know, or explain why you don't have k=0 enough information to answer the question.

2. Consider the power series > ar(x + 2)*. Assume that we know that the series > ak converges, but that k=0 k=0 Ear(1*) diverges. k=0 (a) Does the power series converge at x = -1.3? Explain how you know, or explain why you don't have enough information to answer the question. (b) Does the series > ak(5)* converge or diverge? Explain how you know, or explain why you don't have k=0 enough information to answer the question.

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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2. Consider the power series > ak(x + 2)*. Assume that we know that the series ak converges, but that k=0 k=0 ar(4*) diverges. k=0 (a) Does the power series converge at x = -1.3? Explain how you know, or explain why you don't have enough information to answer the question. (b) Does the series > ak (5)* converge or diverge? Explain how you know, or explain why you don't have k=0 enough information to answer the question.
Transcribed Image Text:2. Consider the power series > ak(x + 2)*. Assume that we know that the series ak converges, but that k=0 k=0 ar(4*) diverges. k=0 (a) Does the power series converge at x = -1.3? Explain how you know, or explain why you don't have enough information to answer the question. (b) Does the series > ak (5)* converge or diverge? Explain how you know, or explain why you don't have k=0 enough information to answer the question.
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