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Series radius

  1. May 1, 2008 #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!
     

    Attached Files:

  2. jcsd
  3. May 1, 2008 #2
    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.
     
  4. May 2, 2008 #3

    HallsofIvy

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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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