Wednesday, October 4, 2017

sequences and series - Proof limntoinftyun+1overun=1+to(un) has a limit ne0

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 limnun+1un=1+




Prove that limnun exists and is 0




Now I tried to use the limit and build from there but to no avail :



ϵ>0,NN:n>N1un+1un1+ϵ



Please provide with a few hints to get me started, thanks a lot !

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