Proving inequalities for these Sequences

[sergey_le]

Homework Statement

Let an be sequences so that an+1-an>-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

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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

 

[member 587159]

It is really time to learn some Latex because this is unreadable. At some point in your scientific career, you will need to use this anyway so might as well learn the basics (takes 5 minuts, just start with putting hashtags around math expressions). See here:

https://www.physicsforums.com/help/latexhelp/

 

[sergey_le]

It is really time to learn some Latex because this is unreadable. At some point in your scientific career, you will need to use this anyway so might as well learn the basics (takes 5 minuts, just start with putting hashtags around math expressions). See here:

https://www.physicsforums.com/help/latexhelp/

Ok I will read it and post my question again.
I know it's hard to understand me either because my English is not good.
Thank you for everything

 

[member 587159]

Ok I will read it and post my question again.
I know it's hard to understand me either because my English is not good.
Thank you for everything

Thanks for putting in effort. This is one of the main characteristic a good student must have!

 

[berkeman]

Ok I will read it and post my question again.

Somewhat improved thread is now posted here: https://www.physicsforums.com/threa...-that-a_n-1-a_n-1-and-a_n-2-for-all-n.983117/

This thread is now locked.