%%
%% The LaTeX Companion, 3ed
%%
%% Example A-1-7 on page II-628 in "Nesting new commands in each other".
%%
%% 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{}
\newcommand\DEFlvec[2]{\renewcommand\lvec[1][#2]%
            {\ensuremath{#1_1+\cdots + #1_{##1}}}}
\DEFlvec{x}{n}  % initial definition
%StopShownPreambleCommands

\begin{document}
Default: $\lvec \neq \lvec[k]$ \par
\DEFlvec{y}{i} Now: $\lvec \neq \lvec[k]$
\end{document}