Results 1 to 2 of 2

Math Help - Convergence of sum

  1. #1
    Senior Member vincisonfire's Avatar
    Joined
    Oct 2008
    From
    Sainte-Flavie
    Posts
    469
    Thanks
    2
    Awards
    1

    Convergence of sum

    Show that if  \sum\limits_{n=0}^\infty a_n^2 and  \sum\limits_{n=0}^\infty b_n^2 converge, then  \sum\limits_{n=0}^\infty a_nb_n converges.
    Without using Cauchy Sharwz inequality?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor chisigma's Avatar
    Joined
    Mar 2009
    From
    near Piacenza (Italy)
    Posts
    2,162
    Thanks
    5
    If we for each n indicate with c_{n}^{2} the greater between a_{n}^{2} and b_{n}^{2}, the series \sum_{n=0}^{\infty} c_{n}^{2} is clearly convergent. But is |a_{n}\cdot b_{n}|\le c_{n}^{2}, so that the series \sum_{n=0}^{\infty} a_{n}\cdot b_{n} is convergent...

    Kind regards

    \chi \sigma
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: May 13th 2010, 01:20 PM
  2. Replies: 2
    Last Post: May 1st 2010, 09:22 PM
  3. dominated convergence theorem for convergence in measure
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: December 5th 2009, 04:06 AM
  4. Replies: 6
    Last Post: October 1st 2009, 09:10 AM
  5. Pointwise Convergence vs. Uniform Convergence
    Posted in the Calculus Forum
    Replies: 8
    Last Post: October 31st 2007, 05:47 PM

Search Tags


/mathhelpforum @mathhelpforum