This is LaTeX code:

[latex]
\left.\begin{array}{c@{\ =\ }l}
\left(0+1\right)^{k+1} & 0^{k+1} + {k+1 \choose 1} \cdot 0^k + {k+1 \choose 2} \cdot 0^{k-1} + \ldots + {k+1 \choose k} \cdot 0 + 1 \\
\left(1+1\right)^{k+1} & 1^{k+1} + {k+1 \choose 1} \cdot 1^k + {k+1 \choose 2} \cdot 1^{k-1} + \ldots + {k+1 \choose k} \cdot 1 + 1 \\
\left(2+1\right)^{k+1} & 2^{k+1} + {k+1 \choose 1} \cdot 2^k + {k+1 \choose 2} \cdot 2^{k-1} + \ldots + {k+1 \choose k} \cdot 2 + 1 \\
\vdots & \vdots
\\
\left(\left(n-1\right)+1\right)^{k+1} & \left(n-1\right)^{k+1} + {k+1 \choose 1} \cdot \left(n-1\right)^k + {k+1 \choose 2} \cdot \left(n-1\right)^{k-1} + \ldots + {k+1 \choose k} \cdot \left(n-1\right) + 1
\\
\left(n+1\right)^{k+1} & n^{k+1} + {k+1 \choose 1} \cdot n^k + {k+1 \choose 2} \cdot n^{k-1} + \ldots + {k+1 \choose k} \cdot n + 1 
\end{array} \right\} +
[/latex]