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Limit of a sequence

  1. Oct 12, 2009 #1
    1. The problem statement, all variables and given/known data
    Suppose that a_n->L as n->infinity. Show that (a1+a2+...+an)/n=L as well.


    2. Relevant equations



    3. The attempt at a solution
    I'm thinking something about limit theorems here?
     
  2. jcsd
  3. Oct 12, 2009 #2
    use the definition. note that |(a1+a2+...+an)/n-L| = |((a1-L)+...+(an-L))/n|, and I guess you know something about the behavior of |a_n-L| when n goes to infinity :)
    hope this helps u
     
  4. Oct 12, 2009 #3
    Sheesh, should have seen that. Thanks!
     
  5. Oct 12, 2009 #4

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    No, you shouldn't have seen that. That's not a proof at all. You need to go back to epsilons and deltas for this one.
     
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