\documentclass{beamer}
\begin{document}
\begin{frame}{Finite difference table}
\begin{center}
\begin{tabular}{c|c|c|c|c|c}
$t_i$ & $f_i$ & $f[t_i,t_{i+1}]$ & $f[t_i,t_{i+1}, t_{i+2}]$ & $f[t_i,\ldots, t_{i+3}]$ & $f[t_i,\ldots, t_{i+4}]$ \\ \hline
0 & -1 & & & & \\
& & -2 & & & \\
0 & -1 & & 3 & & \\
& & -1 & & 6 & \\
1 & 0 & & 9 & & 5 \\
& & 10 & & 11 & \\
1 & 0 & & 20 & & \\
& & 10 & & & \\
1 & 0 & & & & \\
\end{tabular}
\end{center}
\end{frame}
\end{document}
