Results 1 to 2 of 2

Math Help - one more series question

  1. #1
    Newbie
    Joined
    Jan 2008
    Posts
    12

    one more series question

    How would I show this:

    If the series a_n with a_n > 0 is convergent, and if b_n = (a1 + a2 + .... + an)/n for n in N, then show that the series b_n is always divergent.

    Thanks for your help.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by jamesHADDY View Post
    How would I show this:

    If the series a_n with a_n > 0 is convergent, and if b_n = (a1 + a2 + .... + an)/n for n in N, then show that the series b_n is always divergent.

    Thanks for your help.
    b_n = \frac{a_1+\cdots+a_n}{n} \geq \frac{a_1}{n} .

    But, \sum_{n=1}^{\infty} \frac{a_1}{n} = \infty.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. question about answer to fourier series question
    Posted in the Advanced Math Topics Forum
    Replies: 11
    Last Post: February 9th 2011, 12:29 PM
  2. Replies: 0
    Last Post: January 26th 2010, 08:06 AM
  3. Series Question
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 28th 2008, 12:44 AM
  4. Sequences and Series - Power Series Question
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 20th 2008, 07:32 PM
  5. Replies: 6
    Last Post: August 18th 2007, 12:13 PM

Search Tags


/mathhelpforum @mathhelpforum