To use it in math mode you could simply use a \foreach outside a tikzpicture. This would require the pgffor package (only if you're not using Tikz already):

\documentclass[]{article}

\usepackage{mathtools}
\usepackage{pgffor}

\newcommand{\repsum}[3]{%
    \foreach \i in {0,...,#1}{
        \ifnum\i>0
            + #2_{\i} #3_{\i}
        \else
            #2_{\i} #3_{\i}
        \fi
    }
}

\begin{document}
    \begin{equation*}
        \mathbf{F}\bullet\mathbf{u} = \repsum{9}{F}{u}
    \end{equation*}
\end{document}

To use it in math mode you could simply use a \foreach outside a tikzpicture. This would require the pgffor package (only if you're not using Tikz already):

\documentclass[]{article}

\usepackage{mathtools}
\usepackage{pgffor}

\newcommand{\repsum}[3]{%
    \foreach \i in {1,...,#1}{
        \ifnum\i>1
            + #2_{\i} #3_{\i}
        \else
            #2_{\i} #3_{\i}
        \fi
    }
}

\begin{document}
    \begin{equation*}
        \mathbf{F}\bullet\mathbf{u} = \repsum{9}{F}{u}
    \end{equation*}
\end{document}