Math Help - Another real analysis problem.

1. Another real analysis problem.

prove the following:

lim (3n+1/n+2)=3

2. Originally Posted by trojanlaxx223
prove the following:

lim (3n+1/n+2)=3
Let $\epsilon > 0$

Choose $N \in \mathbb{N}$ such that for all $n > N$

$n > \frac{5}{\epsilon} \iff \epsilon > \frac{5}{n}$

$\left| \frac{3n+1}{n+2}-3 \right|=\left| \frac{-5}{n+2}\right|< \frac{5}{n}< \epsilon$