limits of the sequence $n/(n+1)$ Given the problem:
Determine the limits of the sequnce $\{x_n\}^
\infty_{
n=1}$
$$x_n = \frac{n}{n+1}$$
The solution to this is:  
step1:  
$\lim\limits_{n \rightarrow \infty} x_n = \lim\limits_{n \rightarrow \infty} \frac{n}{n + 1}$  
step2:  
$=\lim\limits_{n \rightarrow \infty} \frac{1}{1+\frac{1}{n}}$  
step3:  
$=\frac{1}{1 + \lim\limits_{n \rightarrow \infty} \frac{1}{n}}$  
step4:  
$=\frac{1}{1 + 0}$  
step5:  
$=1$
I get how you go from step 2 to 5 but I don't understand how you go from step 1 to 2.
Again, I'm stuck on the basic highschool math.
Please help

You can also do this way,
$$\begin{eqnarray*} \lim_ {n\to \infty}x_n &=& \lim_{n\to \infty} \frac{n+1-1}{n+1}\\
&=& \lim_{n\to \infty}1-\frac{1}{n+1}\\
&=& 1-\lim_{n\to \infty}\frac{1}{n+1}\\
&=& 1 \end{eqnarray*}$$
because as $n \to \infty$, we have $\frac{1}{n+1} \to 0 .$
