Summation to Infinity in LaTeX (\sum_{n=0}^{\infty})

Where it is used

Sum indexed from n = 0 to infinity, the form used for power series.

Starting at zero is natural for power and Taylor series: e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} and the geometric series \sum_{n=0}^{\infty} r^n = \frac{1}{1-r} for |r| < 1. Check the starting index carefully, since shifting from n = 0 to n = 1 drops the first term and changes the closed form. In display mode the limits are stacked; inline they move beside the sigma. When the upper bound is infinity, \sum_{n \ge 0} is a compact alternative. Generating functions of a sequence a_n are written the same way, \sum_{n=0}^{\infty} a_n x^n.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Summation to Infinity: $\sum_{n=0}^{\infty}$

\[ e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} \]
\end{document}

Related symbols

• Product\prod
• Summation\sum_{i=1}^{n}
• Product\prod_{i=1}^{n}
• Summation\sum
• Coproduct\coprod
• Big Union\bigcup

Frequently asked questions

How do I write Summation to Infinity in LaTeX?

Type \sum_{n=0}^{\infty} in math mode, for example $e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!}$. It works in plain LaTeX without loading any package.

Which package do I need for \sum_{n=0}^{\infty}?

None. \sum_{n=0}^{\infty} is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \sum_{n=0}^{\infty} in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\sum_{n=0}^{\infty}$ in running text.