Results 1 to 2 of 2

Math Help - Cesaro Sum Help

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    15

    Exclamation Cesaro Sum Help

    I apologize if this is in the wrong subject, but it is for my calculus class.

    (a) Let a_n >= 0, n \in N Let s_n = a_1 + a_2 + · · · a_n, i.e., partial sums of \sum a_n from n = 1 to infinity.

    Furthermore, let

     \tau_n = \frac{s_1 + s_2 + ... + s_n}{n} , n \in N.

    Prove:

    If lim  s_n = s then  lim  \tau_n = s as well.

    (b) The \tau_n are called Cesaro sums, and the process is called Cesaro summation. It is used when the original sequence converges slowly or when a series does not have convergent partial sums. For example the series:

    1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, . . .

    s_n does not have convergent partial sums but \tau does converge. Find the Cesaro limit ( lim \tau_n)
    of the sequence.
    Last edited by flipperpk; November 2nd 2009 at 01:28 PM. Reason: typos
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Sep 2009
    Posts
    15
    I figured out how to do part b (compute the Cesaro sum), so now I only need help on

    Prove:

    If then as well.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cesaro summable proof
    Posted in the Calculus Forum
    Replies: 1
    Last Post: April 15th 2010, 06:43 PM
  2. convergence of cesaro averages
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 22nd 2010, 01:02 AM
  3. How to pronounce "Cesāro"?
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: January 23rd 2010, 11:19 AM

Search Tags


/mathhelpforum @mathhelpforum