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:
\[ \textstyle\sum_{i=1}^{n} \]

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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

Related Topics