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Homework Statement:

Let a_n be sequence so that a_n+1a_n>1 and a_n>2 for all n.
1.Prove that if there is a natural N such that a_N is positive, then a_n> 2 for all n
2. From paragraph 1 conclude, that almost all a_n are positive or that almost all a_n are negative.
3. Prove that if for every n is Happening a_n+1<\frac a_n a_1
Relevant Equations:
 
I need help only in section 3
I have some kind of solution but I'm not sure because it seems too short and too simple.
We showed in section 1 that an> 0 per n.
it Given that a_n + 1 <0 and a_n+1<\frac a_n a_1 In addition therefore a_1 <0 is warranted
I have some kind of solution but I'm not sure because it seems too short and too simple.
We showed in section 1 that an> 0 per n.
it Given that a_n + 1 <0 and a_n+1<\frac a_n a_1 In addition therefore a_1 <0 is warranted