In many
\[\begin{equation} \sum_{i=1}^{n} i = \dfrac{n(n+1)}{2} \end{equation}\] \[\begin{equation} | \boldsymbol{\Psi} \rangle = \sum_{i=1}^N a_i | g_i \rangle, \end{equation}\]In many
\[\begin{equation} \sum_{i=1}^{n} i = \dfrac{n(n+1)}{2} \end{equation}\] \[\begin{equation} | \boldsymbol{\Psi} \rangle = \sum_{i=1}^N a_i | g_i \rangle, \end{equation}\]