I am trying to create a Latex document but it isn't formatting correctly and it says there are 31 errors.

\documentclass{article}

\begin{document}

\begin{flushleft}

The sequence \left(\frac{1}{\sqrt{n}}\right)\rightarrow 0. \\

\mbox{For each} \epsilon =0.01, 0.001, 0.0001, \mbox{determine an} \mathbb{Z} \mbox{N with the property that}

\left |\frac{1}{\sqrt{n}}-0\right |<\epsilon, \forall n>N.\\

\left |\frac{1}{\sqrt{n}}\right |<\epsilon\rightarrow n^2>\frac{1}{\epsilon}, \mbox{whenever} n>N\\

\mbox{I obtained:}\\

\begin{vmatrix}\epsilon & 0.01 & 0.001 & 0.0001\\ N & 10 & 10\sqrt{10} & 100\end{vmatrix}\\

\mbox{However, the book has the values of N as 10,0000; 1,000,000; and 100,000,000; respectively.}\\

\end{flushleft}

\end{document}

Can someone let me know the problem?