How to use sigma, summation(Σ) symbol in LaTeX?

A letter of Big Greek alphabet is sigma, in mathematics, it is used as a summation operator.

Differences in output between \Sigma and \sum commands

In latex, you have to use \Sigma command for the small size of sigma and \sum for big size of sigma.

\documentclass{article}
\begin{document}
   \[ \Sigma \]
   \[ \sum \]
\end{document}

Sigma symbol with limits

You can use the \Sigma_{subscript}^{superscript} command to use limits with the sigma symbol. But it is not a good practice.

\documentclass{article}
\begin{document}
   \[ \Sigma_{i=1}^{100} i \]
   \[ \Sigma_{i=1}^n =kn \]
   \[ \Sigma_{i=1}^\infty \]
\end{document}

Use sum command with limits

In the example above you can see that the best result is not coming in the case of using limits or it does not look so professional.

So in this case you can use the \sum command and use the \sum_{subscript}^{superscript} command to use the limits with the symbol.

\documentclass{article}
\begin{document}
   \[ \sum_{i=1}^{100} i \]
   \[ \sum_{i=1}^n =kn \]
   \[ \sum_{i=1}^\infty \]
\end{document}

Create command for sigma with limits

You can create a custom latex command using the \newcommand{}[]{} command to simplify the process.

You can also use the \limits command, no problem if you don’t use it but it is a good practice to use it to set limits. Below are some examples.

\documentclass{article}
\newcommand{\summation}[2]{\sum\limits^{#1}_{#2}}
\begin{document}
   \[ \sqrt{\frac{1}{N}\summation{N}{i=1}(x_i -\mu)} \]
   \[ \summation{n}{i=1} i=\frac{n(n+1)}{2} \]
\end{document}