+00 (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.
+00 (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.
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 11TI: Determine whether the sum of the infinite series is defined. k=115(0.3)k
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With explanation and full solution please
![(x + 7)"
2n Vn2 – 1
Consider the power series >
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff0d1863-00d4-4b9d-8de4-c254d5397687%2Fae27af46-676a-488b-a0db-70e3a0c76c67%2F2ztzytq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(x + 7)"
2n Vn2 – 1
Consider the power series >
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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