Results 1 to 3 of 3

Math Help - When is this power series convergent?

  1. #1
    Junior Member
    Joined
    Oct 2010
    Posts
    43

    When is this power series convergent?

    For which x \in R is it convergent?

    \sum\limits_{n=0}^\infty(-1)^n \frac{(x-2)^n}{5n9^n}

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,655
    Thanks
    1601
    Awards
    1
    \displaystyle\sqrt[n]{{\frac{{\left| {x - 2} \right|^n }}{{5n9^n }}}} \to ?<1
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Also sprach Zarathustra's Avatar
    Joined
    Dec 2009
    From
    Russia
    Posts
    1,506
    Thanks
    1
    First, find the radius of convergence...

    R=\mid\frac{a_n}{a_{n+1}}\mid

    Then...

    -R<x-2<R

    Check:

    x=R, x=-R
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: April 25th 2010, 08:46 PM
  2. Convergent power series of (x^2)-(c^2)?
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 3rd 2009, 07:52 AM
  3. Replies: 3
    Last Post: April 6th 2009, 10:03 PM
  4. find convergent set of the power series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 31st 2007, 04:06 PM
  5. find convergent set of the power series
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 31st 2007, 05:47 AM

Search Tags


/mathhelpforum @mathhelpforum