Results 1 to 2 of 2

Math Help - Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    18

    Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent

    Given the infinite series xn is absolutely convergent, show that the infinite series xn/(1+xn) is absolutely convergent.

    I am completely stumped, I have tried using properties of the limit test and the comparison test to show this, but I can't seem to make any progress,
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member girdav's Avatar
    Joined
    Jul 2009
    From
    Rouen, France
    Posts
    678
    Thanks
    32

    Re: Series Absolutely Convergent, xn/(1+xn^2) absolutely convergent

    Since the series \sum_n |x_n| is convergent, we have in particular that |1+x_n|\geq \frac 12 for n large enough. Hence we have 0\leq \left|\frac{x_n}{1+x_n}\right|\leq 2|x_n|, and you can conclude.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: May 2nd 2010, 03:25 AM
  2. Replies: 1
    Last Post: April 25th 2010, 08:46 PM
  3. Replies: 3
    Last Post: April 6th 2009, 10:03 PM
  4. Replies: 8
    Last Post: February 21st 2009, 09:16 AM
  5. absolutely convergent series
    Posted in the Calculus Forum
    Replies: 7
    Last Post: November 15th 2008, 06:01 PM

Search Tags


/mathhelpforum @mathhelpforum