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Convergence of sequences

  1. Sep 11, 2011 #1
    1. The problem statement, all variables and given/known data
    let (An) be a sequence in R with |summation from n=1 to infinity(An)|< infinity. Prove lim as n goes to infinity of ((A1 +2A2+...+nAn)/n) = 0


    2. Relevant equations



    3. The attempt at a solution
    I think |summation from n=1 to infinity(An)|< infinity means the summation converges .I rewrote " lim as n goes to infinity of ((A1 +2A2+...+nAn)/n) = 0 " as "lim as n goes to infinity of ((summation from k=1 to n of nAn)/n)=0. Since I assmumed "summation from n=1 to infinity(An)" converges, that would imply the lim of An is 0. I dont know how to use this info to prove what i need to prove. Hope you can understand this. I dont know how to use tek.
     
  2. jcsd
  3. Sep 11, 2011 #2
    Hint: If the summation of An converges and for all n ,Bn<An, then the summation of Bn converges.
     
  4. Sep 11, 2011 #3
    Forgive my missing absolute. |Bn|<|An|
     
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