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.
Integer and sum limits improvement. In inline math mode the integral/sum/product lower and upper limits are placed right of integral symbol. Similar is for limit expressions. If you want the limits of an integral/sum/product to be specified above and below the symbol in inline math mode, use the \limits command before limits specification.
In textstyle the limits (the n=1 in that case) are pushed to the right of the operator, while in displaystyle it is above and below.. The style used to display the formula depends on where it is in the text (inline in text or in an equation-like environment), and where it is in the formula (for example, in matrices or fractions, the subformulas are in text style by default).
In a similar manner to the summation symbol, the product symbol can easily be added to a LaTeX document using the \prod notation.The sybmol can be compressed to fit on one line (useful for small equations displayed within a text block), or enlarged to make it more readable.
This command generates the product operator, $ \prod $. The difference between this and \Pi, which generates the capital letter $ \Pi $, is that \product appears larger, and that it supports the limits to be displayed below and above the symbol. The following example illustrates the difference.