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Homework Statement:

Let an be sequences so that an+1an>1 and an>2 for all n.
1.Prove that if there is a natural N such that aN is positive, then an> 2 for all
2. From paragraph 1, conclude that almost all organs are positive or that almost all organs are negative.
3. Prove that if every n exists an+1<an/a1 than a1<0
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.
Given that an + 1 <0 and an + 1 = an / a1 therefore a1 <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.
Given that an + 1 <0 and an + 1 = an / a1 therefore a1 <0 is warranted