Series radius

  • #1
I am hopelessly confused on a homework assignment.

The problem says " (a) Find the series radius and interval of convergence. For what values of x does the series converge (b) absolutely, (c) conditionally?"

Attached is a sample of problems from the book.

Any help would be appreciated!
 

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Answers and Replies

  • #2
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4
These are power series. The radius of convergence is

[tex]\lim_{x\to\infty}\left|\frac{a_n_+_1}{a_n}\right|[/tex] then the series converges for


[tex]\lim_{x\to\infty}\left|\frac{a_n_+_1}{a_n}\right|<1[/tex]

After that you find that the series converges say for x in the interval (a,b) and after that try to test whether the series converges at a and b, by letting x=a, and x=b respectively.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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The series converges absolutely inside the radius of convergence, diverges outside and may converge absolutely, converge conditionally, or diverge at the endpoints. That's why you have to test those separately.
 

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