$
\begin{array}{l}
\sum\limits_{k = 0}^{10} {\left( {\begin{array}{*{20}c}
{10} \\
k \\
\end{array}} \right) \cdot \left( {\frac{1}{2}} \right)^{10} } = \\
\left( {\begin{array}{*{20}c}
{10} \\
0 \\
\end{array}} \right) \cdot \left( {\frac{1}{2}} \right)^{10} + \left( {\begin{array}{*{20}c}
{10} \\
1 \\
\end{array}} \right) \cdot \left( {\frac{1}{2}} \right)^{10} + ... + \left( {\begin{array}{*{20}c}
{10} \\
{10} \\
\end{array}} \right) \cdot \left( {\frac{1}{2}} \right)^{10} \\
\left( {\frac{1}{2}} \right)^{10} \cdot \left( {\left( {\begin{array}{*{20}c}
{10} \\
0 \\
\end{array}} \right) + \left( {\begin{array}{*{20}c}
{10} \\
1 \\
\end{array}} \right) + ... + \left( {\begin{array}{*{20}c}
{10} \\
{10} \\
\end{array}} \right)} \right) \\
\left( {\frac{1}{2}} \right)^{10} \cdot 2^{10} = 1 \\
\end{array}
$
Dat was niet echt een verrassing of toch?
WvR
27-12-2018