Representation of $0$ as $\sum \sp{N}\sb{K=-N}\,\varepsilon \sb{k}k$

If <!-- MATH ${\varepsilon _k}$ --> are independent identically distributed random variables with values 0 and , each with probability <!-- MATH $\tfrac{1} {2}$ --> then <!-- MATH \begin{displaymath} P\left( {\sum\limits_{k = - N}^{ + N} {{\varepsilon _k}k = 0} } \right) \sim {\left( {\frac{3} {\pi }} \right)^{1/2}}{N^{ - 3/2}}. \end{displaymath} -->