How to type the three dots in a product?

Use \cdots. (See also: \vdots and \ddots.)

Edit

Actually, I just read in the «Short Math Guide for LaTeX» by the AMS that:

• \dotsc is for dots with commas,
• \dotsb is for dots with binary operators,
• \dotsm is for multiplication dots,
• \dotsi is for dots with integrals,
• \dotso is for other dots.

So, \cdots and \ldots are commonly used but the AMS convention is to use the more semantic commands.

Or you can use \dots which can be used both inside and outside of math-mode.