\left( \begin{array}{l}
 n \\ 
 1 \\ 
 \end{array} \right) - \left( \begin{array}{l}
 n \\ 
 3 \\ 
 \end{array} \right) + \left( \begin{array}{l}
 n \\ 
 5 \\ 
 \end{array} \right) - \left( \begin{array}{l}
 n \\ 
 7 \\ 
 \end{array} \right) + ... = \sqrt {2^n } \sin \frac{{n\pi }}{4} \\ 
 \end{array}
\]