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