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Prove inequality about sequences

  1. Mar 9, 2008 #1
    1. The problem statement, all variables and given/known data
    Let [tex]u_n, v_n[/tex] be a sequence of positive real number such that
    [tex]u_{n+1}\leq (1+v_n)u_n[/tex] where [tex]\sum_{n=1}^{\infty}v_n[/tex]
    converges.

    It is true or false if true please help me prove.
    if [tex]\frac{u_{n+1}}{u_n}\leq M [/tex] then [tex]u_n\leq M[/tex]
    for some [tex]M[/tex] be a positive real number.

    whether we can find [tex]M[/tex] is a positive real number such that
    [tex]u_n\leq M[/tex] for all natural number n


    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
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