Prove that if $\epsilon > 0$ is given, then $\frac{n}{n+2}$ ${\approx_\epsilon}$ 1, for $n$ $\gg$1.
Olivia Zamora 
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The book I am using for my Advance Calculus course is Introduction to Analysis by Arthur Mattuck.
Prove that if $\epsilon > 0$ is given, then $\frac{n}{n+2}$ ${\approx_\epsilon}$ 1, for $n$ $\gg$1.
This is my rough proof to this question. I was wondering if anybody can look over it and see if I made a mistake or if there is a simpler way of doing this problem. I want to thank you ahead of time it is greatly appreciated.So lets begin:
Proof:
1 Answer
$\begingroup$$$ \forall n>1, \,\,\,\,\,1-\frac{2}{n}<\frac{n}{n+2}<1. $$
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