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Homework Help: Limit proof

  1. Mar 22, 2012 #1
    Be {xn} a sequence that satisfies the condition 0 ≤ [itex]x_{m+n}[/itex] ≤ [itex]x_{m}[/itex] + [itex]x_{n}[/itex]. Prove that [itex]lim_{n ->∞}[/itex] xn/n exists.

    I'm kind of lost in this.
     
  2. jcsd
  3. Mar 22, 2012 #2

    Dick

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    I would start by thinking like this:

    x2<=x1+x1

    x3<=x2+x1<=x1+x1+x1

    etc. What can you make of that?
     
  4. Mar 25, 2012 #3
    Ughh I'm still lost :S
     
  5. Mar 25, 2012 #4

    I like Serena

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    Hi cristina89! :smile:

    Can you write xn in the form that Dick suggested?
     
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