Summation in LaTeX: \sum
Use \sum with subscripts and superscripts to typeset summation notation in LaTeX.
Quick answer
latex
% Inline: $\sum_{i=1}^{n} i$
% Display (limits above/below):
\[ \sum_{i=1}^{n} i = \frac{n(n+1)}{2} \]Common summation formulas
latex
% Sum of integers:
\[ \sum_{i=1}^{n} i = \frac{n(n+1)}{2} \]
% Sum of squares:
\[ \sum_{i=1}^{n} i^2 = \frac{n(n+1)(2n+1)}{6} \]
% Geometric series:
\[ \sum_{k=0}^{\infty} r^k = \frac{1}{1-r}, \quad |r| < 1 \]
% Double sum:
\[ \sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij} \]Inline vs display mode
In inline math, limits appear beside the sigma to avoid increasing line height. In display mode they move above/below.
latex
% Inline (compact): $\sum_{i=1}^{n}$
% Display (full size):
\[ \sum_{i=1}^{n} \]
% Force display style inline:
$\displaystyle\sum_{i=1}^{n}$
% Force inline style in display:
\[ \textstyle\sum_{i=1}^{n} \]Summation with conditions
latex
% Sum over a set:
\[ \sum_{x \in S} f(x) \]
% Sum with condition:
\[ \sum_{\substack{i=1 \\ i \neq j}}^{n} a_i \]
% Sum over primes:
\[ \sum_{p \text{ prime}} \frac{1}{p} \]Related operators
latex
\prod_{i=1}^{n} i % product (Π)
\bigcup_{i=1}^{n} A_i % union
\bigcap_{i=1}^{n} A_i % intersection
\bigoplus_{i=1}^{n} V_i % direct sum
\int_a^b f(x)\,dx % integral