\documentstyle[12pt]{article}
\pagestyle{empty}
\begin{document}

\begin{eqnarray*}
   U^{cond} = \displaystyle\sum_{i=1}^{N} u_{i}^{cond} \\ 
   U^{mech} = \displaystyle\sum_{i=1}^{N} u_{i}^{mech} \\
   U = \displaystyle\sum_{i=1}^{N} (u_{i}^{cond} + u_{i}^{mech}) \\
   \theta_{avg} = (\frac{1}{N}\displaystyle\sum_{i=1}^{N} \frac{1}{\theta_{i}})^{-1} \\
\end{eqnarray*}                           

\end{document}