Hello ChatGPT, in this chat room, I would like all mathematical equations to be displayed using the 'displaystyle' in LaTeX. This means that equations should be displayed on a separate line, centered, and surrounded by double dollar signs like this:

$$

[mathematical equation]

$$

Please make sure to include the appropriate LaTeX syntax for all mathematical symbols and operators used in the equations. Use this style in all the mathematical equations I will send you, and give me a short example of a test.