# On Fekete's Lemma

1. Oct 22, 2009

### CoachZ

Fekete's Lemma states that if {a_n} is a real sequence and a_(m + n) <= a_m + a_n, then one of the following two situations occurs:
a.) {(a_n) / n} converges to its infimum as n approaches infinity
b.) {(a_n) / n} diverges to - infinity.

I'm trying to figure out a way to show either of these things happen but can't seem to do it. Does anyone have the proof of this or have suggestions to go about proving it.

2. Oct 23, 2009

### foxjwill

a) Suppose the {a_n/n} converges to some number A. Show that A is the inf.