Note that I do not actually recommend you do the following. But, since you ask: You can force TeX/LaTeX to issue the directive \displaystyle automatically whenever you initiate inline-math mode -- via either an opening-$ or a \( instruction -- by inserting the following command in your document's preamble:
\everymath{\displaystyle}
Again, I do not recommend you take this route. There are excellent typographic reasons for not using large summation, product, and integral symbols while in inline-math mode. Likewise, it's almost invariably a bad idea to typeset display-style fraction constructs while in inline math mode.
For much more information on this matter, I suggest you take a look at the posting Show inline math as if it were display math.
I can think of only one exception to the broad stricture against the automatic use of \displaystyle: In beamer-class documents, it is quite important not to let the math symbols become too small. One way of achieving this is to use \displaystyle throughout. Even for beamer documents, though, providing the instruction \everymath{\displaystyle} may be too much of a good thing.
Addendum, prompted by a follow-up comment by the OP: To revert back to "text style" while in inline math mode, just issue the command \textstyle. The following MWE illustrates the look of various math objects if \displaystyle and \textstyle are in effect:

\documentclass{article}
\everymath{\displaystyle} % automatically use display style while in inline math mode
\begin{document}
$\sum \quad \prod \quad \int \quad \frac{abc}{xyz}$
$\textstyle\sum \quad \prod \quad \int \quad \frac{abc}{xyz}$
\end{document}
\everymath{\displaystyle}in the preamble... This will insert a\displaystyledirective every time inline-math is initiated. – Mico Feb 19 '14 at 13:21$$ math $$, please use\[ a+b \]instead. – Johannes_B Feb 19 '14 at 13:24\(and\)– Steven B. Segletes Feb 19 '14 at 13:27\displaystyleall over in the first place? I've never come across any users who needed that. – daleif Feb 19 '14 at 13:30$ math $or\( math \)) or\[ math \]for displaymath (on its own line, unnumbered). If you want to change the appearance of displayed math, there are various options. Consult Herbert Voß' Math mode. – Johannes_B Feb 19 '14 at 13:36:)– Svend Tveskæg Feb 19 '14 at 14:04\displaystyleif you are needing it perhaps something is wrong elsewhere in your markup. – David Carlisle Feb 19 '14 at 15:04\dfraccommand from theamsmathpackage, which typesets a fraction with large numerator and denominator no matter where it is. – Charles Staats Feb 19 '14 at 16:06