TITLE: Simplifying product of differences
QUESTION [10 upvotes]: How do we simplify this?  Confused.
$$\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right)\cdots\left(1-\frac{1}{n}\right)$$

REPLY [13 votes]: Why didn't you even try for small numbers? If you had, you could have canceled out all the terms. ;)
The expression turns out to be  
$\dfrac{2}{3}.\dfrac{3}{4}.\dfrac{4}{5} \dots\dfrac{n-2}{n-1}.\dfrac{n-1}{n}$
Cancel out the terms and you're left with just $\frac{2}{n}$.