$x_n= \sqrt{\frac{n+1}{n}}$where $x_n$ is the $n^{th}$ term in the sequence.
Now, $x_n \rightarrow 1$ as $n\rightarrow\infty$.
Then applying definition of limit: $\left|\sqrt{\frac{n+1}{n}}- 1 \right|= \frac{\frac{n+1}{n}-1}{\sqrt{\frac{n+1}{n}}+1}<\frac{1}{2n}<\epsilon$
whenever $n>N=1/(2\epsilon)$.
-The difficulty for me is inability to understand how $1/(2n)$ was deduced.
Thank you for assistance and apologies for poor notations
the equation in the code should read after absolute value equation = {[(n+1)/n]-1}/{([(n+1)/n]^0.5)+1}<1/2n< epsilon