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12.8 Power Series. Radius and interval of convergence

12.8 Power Series. Radius and interval of convergence. Mathboat.com. Test endpoints. Ratio Test. (A) (B) (C) (D) (E). Terms of this alternating series are positive, decreasing and n th term approaches 0. Converges by AST. SOLUTION. Ratio Test. Test endpoints. Diverges by BCT.

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12.8 Power Series. Radius and interval of convergence

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  1. 12.8 Power Series. Radius and interval of convergence Mathboat.com

  2. Test endpoints Ratio Test (A) (B) (C) (D) (E) Terms of this alternating series are positive, decreasing and n th term approaches 0. Converges by AST.

  3. SOLUTION

  4. Ratio Test Test endpoints Diverges by BCT Harmonic, Diverges Terms of this alternating series are positive, decreasing and n th term approaches 0. Converges by AST.

  5. Test endpoints (A) (B) (C) (D) (E) Diverges, sum=1 or 0 Ratio Test diverges. sum doesn’t stop growing

  6. SOLUTION

  7. (A) 0 (B) 3 (C) 4 (D) 5 (E) none Test endpoints Terms of this alternating series are positive, decreasing and n th term approaches 0. Converges by AST. Eliminate D

  8. (A) (B) (C) (D) (E) Ratio Test Test endpoints alternating harmonic series converges by AST Harmonic series, diverges

  9. 8.What is the radius of convergence of The radius of convergence is

  10. 9. What are all the values of x for which the series converges? Check Endpoints

  11. 10. What are all values of x for which the series converges? Check Endpoints

  12. Absolutely Converges if Check endpoints! Use Ratio Test Omit negatives in absolute value Harmonic divergent Converges by AST; Alternating Harmonic

  13. Use Ratio Test  Converges only if x = 0

  14. Use Ratio Test 0 0 is always < 1  Converges for all real numbers

  15. Remember: Interval of Convergence is Remember: Interval of Convergence is Use Ratio Test Check endpoints! Converges by AST Find the Radius of Convergence! Find the Radius of Convergence! L’Hopitals Rule Use Basic Comparison Test harmonic divergent diverges too

  16. Interval: Remember: Interval of Convergence is 15. Check endpoints! Use Ratio Test Find the Radius of Convergence! diverges diverges

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