Results 1 to 2 of 2

Math Help - Series-Interval of Convergence-absolutely or conditionally

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    1

    Series-Interval of Convergence-absolutely or conditionally

    Hi everyone I just had a general question. I know that one way to find the interval of convergence for a power series is through the ratio test. If your answer for the test is less then 1 then the series is absolutely convergent. Then you have to check the end points to see if they converge. My question is the following can the endpoints converge conditionally at the endpoints, while in between the endpoints the series converges absolutely? And can you see this just by using the Alternate Series Test on the endpoints after doing the Ratio Test?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,387
    Thanks
    52
    Quote Originally Posted by Mente View Post
    Hi everyone I just had a general question. I know that one way to find the interval of convergence for a power series is through the ratio test. If your answer for the test is less then 1 then the series is absolutely convergent. Then you have to check the end points to see if they converge. My question is the following can the endpoints converge conditionally at the endpoints, while in between the endpoints the series converges absolutely? And can you see this just by using the Alternate Series Test on the endpoints after doing the Ratio Test?
    Typically when you test the endpoints, one of three possibilities happen:

    1) The series converges at both endpoints, e.g. \sum_{n=1}^\infty \frac{x^n}{n^2} so here -1 \le x \le 1

    2) The series converges at only one endpoint, e.g. \sum_{n=1}^\infty \frac{x^n}{n} so here -1 \le x < 1

    3) The series converges at neither endpoints, e.g. \sum_{n=1}^\infty x^n so here -1 < x < 1.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 25th 2010, 09:46 PM
  2. Replies: 3
    Last Post: April 6th 2009, 11:03 PM
  3. Replies: 2
    Last Post: April 26th 2008, 11:48 AM
  4. Series Convergence Conditionally or absolutely
    Posted in the Calculus Forum
    Replies: 28
    Last Post: April 21st 2008, 04:43 PM
  5. Replies: 0
    Last Post: January 23rd 2007, 09:03 PM

Search Tags


/mathhelpforum @mathhelpforum