Results 1 to 1 of 1

Math Help - test

  1. #1
    Newbie
    Joined
    Oct 2013
    From
    DC
    Posts
    6

    Convergent a_n implies convergent (1/n)(a_n + a_{n+1} + ...)

    Let \sum\limits_{n=1}^\infty a_n be a convergent series in which a_n \ge 0, \forall n=1,2, .... Prove that the series \sum\limits_{n=1}^\infty \frac{1}{n} (a_n + a_{n+1} + ... + a_{2n-1}) converges as well.

    How should I start?
    Last edited by bobcantor1983; October 10th 2013 at 06:53 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Limit infina of ratio test and root test
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 23rd 2013, 04:08 PM
  2. Replies: 2
    Last Post: May 21st 2010, 10:56 AM
  3. Replies: 8
    Last Post: March 28th 2010, 06:45 PM
  4. Replies: 7
    Last Post: June 4th 2009, 10:33 PM
  5. ratio test (series) urgent test tommorow!
    Posted in the Calculus Forum
    Replies: 3
    Last Post: December 2nd 2008, 04:27 PM

Search Tags


/mathhelpforum @mathhelpforum