Proving Existence of Limit of Sequence {xn}

[cristina89]

Be {xn} a sequence that satisfies the condition 0 ≤ $x_{m+n}$ ≤ $x_{m}$ + $x_{n}$. Prove that $lim_{n ->∞}$ xn/n exists.

I'm kind of lost in this.

 

[Dick]

Be {xn} a sequence that satisfies the condition 0 ≤ $x_{m+n}$ ≤ $x_{m}$ + $x_{n}$. Prove that $lim_{n ->∞}$ xn/n exists.

I'm kind of lost in this.

I would start by thinking like this:

x2<=x1+x1

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

etc. What can you make of that?

 

[cristina89]

Ughh I'm still lost :S

 

[I like Serena]

Hi cristina89!

Can you write x_n in the form that Dick suggested?