Sum-class symbol

Sum-class symbols, or accumulation symbols, are symbols whose sub- and superscripts appear directly below and above the symbol rather than beside it. For example, the following example illustrates that \sum is one of these elite symbols whereas \Sigma is not. The terminology from AMS-LaTeX documentation.

Table of sum-class symbols

$\int$  \int $\oint$  \oint $\bigcap$  \bigcap $\bigcup$  \bigcup

$\bigodot$  \bigodot $\bigoplus$  \bigoplus $\bigotimes$  \bigotimes $\bigsqcup$  \bigsqcup

$\biguplus$  \biguplus $\bigvee$  \bigvee $\bigwedge$  \bigwedge $\coprod$  \coprod

$\prod$  \prod Failed to parse (unknown function "\smallint"): {\displaystyle \smallint}   \smallint $\sum$  \sum

Using sum

LaTeX markup...	...results in:	...is used for:
\sum\limits_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}	$\sum\limits_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}$	the \limits tag puts the limits below and above the sigma symbol. It is typically used in equations
\sum\nolimits_{i=1}^n i^2 = \frac{n(n+1)(2n+1)}{6}	$\sum \nolimits _{i=1}^{n}i^{2}={\frac {n(n+1)(2n+1)}{6}}$	the \nolimits tag puts the limits on the right of the sigma symbol. It is typically used in the math wired in the text

TeX is smart enough to only show \sum in its expanded form in the displaymath environment. In the regular math environment, \sum does the right thing and revert to non-sum-class behavior, thus conserving vertical space.

Using prod

Another common sum-class symbol is \prod. As in \sum we can use the directive \limits or \nolimits in order to show the limits on top-down or on the right.

LaTeX markup...	...results in:	...is used for:
\prod\limits_{i=1}^n x = x^n	$\prod\limits_{i=1}^n x = x^n$	the product of a sequence of factors