1. Given the sequence $\left\{\frac{n+1}{n+2}\right\}$, for any $e>0$, take $\mathbf{N}=$ $\qquad$ $\sim$, then when $n>N$, it always holds that $\qquad$ $<\varepsilon$, so the limit of the sequence $\left\{\frac{n+1}{n+2}\right\}$ is 1.
1. The integer part of $\left(\frac{1}{\varepsilon}-2\right)$, $\left|\frac{n+1}{n+2}-1\right|$,