1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Doubly Indexed Array

  1. Dec 3, 2007 #1
    HELLO. GOT A QUICK QUESTION:

    FROM THE TEXT:

    [tex]|S_{mn} - S| <\ \in\ for\ all\ m,n \ge N.[/tex]

    [tex]For\ the\ moment,\ consider\ m\ \in\ N\ to\ be\ fixed\ and\ write\ S_{mn}\ as:[/tex]

    [tex]S_{mn}\ =\ \sum^{n}_{j=1}a_{1j}\ +\ \sum^{n}_{j=1}a_{2j}\ +\ ...\ +\ \sum^{n}_{j=1}a_{mj}[/tex]

    [tex]Our\ hypothesis\ guarantees\ that\ for\ each\ fixed\ row,\ i,\ the\ series\ \sum^{\infty}_{j=1}\ converges\ absoloutely\ to\ some\ real\ number,\ r_i.[/tex]

    HERES WHAT I HAVE TO DO:

    [tex]Exercise\ 2.8.5.\ (a)\ Use\ the\ Algebraic\ Limit\ Theorem\ and\ the\ Order\ limit\ theorem\ to\ show\ that\ for\ all\ m\ge N\ |(r_{1},\ +\ r_{2},\ +\ ...\ +\ r_{m})\ -\ S| \le \in[/tex]

    [tex]Conclude\ that\ the\ iterated\ sum\ \sum^{\infty}_{i=1}\sum^{\infty}_{j=1}\ converges\ to\ S[/tex]

    Obviously the larger of an m you take r_m to means the closer you'll get to S, and since m belongs to N then the largest it can go is infinity, which would mean the double sum would indeed converge to S. Is that "enough" of a conclusion?
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Doubly Indexed Array
  1. Double Index Array (Replies: 3)

  2. Array correlation (Replies: 0)

  3. Index Sets (Replies: 3)

Loading...