The size of some mathematical symbols, notably summation signs, product signs, and integral signs, depends on the environment in which they appear (i.e., displaymath as opposed to math environments; see Math Formulas and Math Fonts and Styles).
The \sqrt command also produces a variable size symbol appropriate for the size of the radicand argument.
The "limits" associated with these symbols are entered as subscripts for entries appearing below the symbol and as superscripts for entries appearing above the symbol. For example the sum from n=0 to infinity of xn would be entered as ,/p>
The actual placement of the limits depends on whether this is in displaymath mode in which case they are placed below/above or in math mode in running text in which case they are placed as regular subscripts and superscripts.
Note that it is possible to treat several of these symbols (a common example would be a double sum) as a single symbol for placing limits above and/or below by using the \mathop command.
"Hats" and "tildes" over symbols which stretch (as best they can) to the correct size for their arguments are produced by \widehat and \widetilde.
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