power series

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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Please answer part 3, and part 4. Thank you!

+o0
(x + 7)"
Consider the power series >.
2" Vn2 – 1
n=2
1. Use Limit Comparison Test to show that the series diverges when x = -5.
2. Use Alternating Series Test to show that the series converges when x = -9.
3. Is the convergence of the series at x = -9 absolute or conditional? Explain why.
4. Determine the radius and interval of convergence of the power series.
Transcribed Image Text:+o0 (x + 7)" Consider the power series >. 2" Vn2 – 1 n=2 1. Use Limit Comparison Test to show that the series diverges when x = -5. 2. Use Alternating Series Test to show that the series converges when x = -9. 3. Is the convergence of the series at x = -9 absolute or conditional? Explain why. 4. Determine the radius and interval of convergence of the power series.
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