first chunk of compute commands to be converted to use embedded math

\documentclass[12pt]{article}

\begin{document}

$$

   CS = \sum_{i = 1}^{N/2} | \vec{R}_i + \vec{R}_{i+N/2} |^2

$$

\end{document}

\documentclass[12pt,article]{article}

\usepackage{indentfirst}

\usepackage{amsmath}

\begin{document}

\begin{eqnarray*}

  r_{c}^{fcc} & = & \frac{1}{2} \left(\frac{\sqrt{2}}{2} + 1\right) \mathrm{a} \simeq 0.8536 \:\mathrm{a} \\

  r_{c}^{bcc} & = & \frac{1}{2}(\sqrt{2} + 1) \mathrm{a} \simeq 1.207 \:\mathrm{a} \\

  r_{c}^{hcp} & = & \frac{1}{2}\left(1+\sqrt{\frac{4+2x^{2}}{3}}\right) \mathrm{a}

\end{eqnarray*}

\end{document}