Results 1 to 2 of 2

Math Help - Radius/Interval of Convergence

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    186

    Radius/Interval of Convergence

    We were being taught this subject today, however, the professor did not get to finish the lecture and mentioned something about testing the end points of the interval with another test of convergence, so they function doesn't diverge at the end points? How would I do this, as in checking the end points properly, just want to get a step ahead,

    I was given the following example I reworked myself till I obtained the interval of convergence

    \sum_{n=1}^{\infty}\frac{(2x+3)^n}{n^2}

    I implemented a ratio test, here the end result

    |2x-3|\lim_{n\to\infty}(\frac{n}{n+1})^2

    |2x-3|\lim_{n\to\infty}(1-\frac{1}{n+1})^2 = 1

    = |2x+3|

    -1\le2x+3\le1

    -2\le x \le -1
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Dec 2008
    Posts
    319
    Here is a hint: the series at x=-2 and x=-1 are

    \sum_{n=1}^{\infty}\frac{(-1)^n}{n^2}=-1+\frac{1}{2^2}-\frac{1}{3^2}+\frac{1}{4^2}-\cdots

    and

    \sum_{n=1}^{\infty}\frac{1}{n^2}=1+\frac{1}{2^2}+\  frac{1}{3^2}+\frac{1}{4^2}+\cdots.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 1st 2010, 09:22 PM
  2. radius and interval of convergence
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 7th 2009, 12:44 PM
  3. Radius and interval of convergence?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 30th 2009, 08:08 PM
  4. Radius and Interval of Convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 24th 2009, 03:30 PM
  5. Radius and interval of convergence
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 25th 2009, 01:30 AM

Search Tags


/mathhelpforum @mathhelpforum