EDIT : I have doubts about the 1+ notation so I'll come back here as soon as I got the answer. In the mean time please consider this question on hold. Feel free to comment if you have any inputs on the 1+ notation, thanks.
First of all I want to let you know that this is an homework assignment I was given.
So here is the question :
Given (un)n a sequence of strictly positive reals so that limn→∞un+1un=1+
Prove that limn→∞un exists and is ≠0
Now I tried to use the limit and build from there but to no avail :
∀ϵ>0,∃N∈N:n>N→1≤un+1un≤1+ϵ
Please provide with a few hints to get me started, thanks a lot !
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