%%
%% The LaTeX Companion, 3ed
%%
%% Example A-1-6 on page II-626 in "Commands with one optional argument".
%%
%% Copyright (C) 2022 Frank Mittelbach
%%
%% It may be distributed and/or modified under the conditions
%% of the LaTeX Project Public License, either version 1.3c
%% of this license or (at your option) any later version.
%%
%% See https://www.latex-project.org/lppl.txt for details.
%%

\documentclass{tlc3exa}
\pagestyle{empty}
\setcounter{page}{6}
\setlength\textwidth{183.0pt}
%StartShownPreambleCommands
\newcommand\lvec[2][n]
    {\ensuremath{#2_1+\cdots + #2_{#1}}}
%StopShownPreambleCommands

\begin{document}
For the series \lvec{x}  we have
\[ \lvec{x} = \sum_{k=1}^{n} G_{\lvec[k]{y}} \]
\end{document}
