LaTeX tables: Example 2

\begin{tabular}{|c||ccc||r|}
	\hline
\textbf{\em k}  &  $x_1^k$    &   $x_2^k$  & $x_3^k$ & remarks    \\
	\hline \hline
0   & -0.30000000 & 0.60000000 & ~0.70000000 & $x^0$ \\
1   & ~0.47102965 & 0.04883157 & -0.53345964 &   \\
2   & ~0.49988691 & 0.00228830 & -0.52246185 &   \\
3   & ~0.49999976 & 0.00005380 & -0.52365600 & $\epsilon<\delta$ \\
4   & ~0.50000000 & 0.00000307 & -0.52359743 & ($\forall n>N$) \\
	\hline
7   & ~0.50000000 & 0.00000000 & -0.52359878 & $\epsilon\ll\zeta$ \\
	\hline
\end{tabular}