N + 1 = \sum\limits_{i = 1}^k {\left( \begin{array}{c}
x_i \\
i \\
\end{array} \right)} + 1 = \sum\limits_{i = 2}^k {\left( \begin{array}{c}
x_i \\
i \\
\end{array} \right)} + \left( \begin{array}{c}
x_1 \\
1 \\
\end{array} \right) + \left( \begin{array}{c}
x_1 \\
0 \\
\end{array} \right) = ... = \left( \begin{array}{c}
x_k + 1 \\
k \\
\end{array} \right) |