TITLE: What does "$\cdots$" mean in $\frac{n(n-1)(n-2)\cdots(n-r+2)}{(r-1)!}a^{n-r+1}b^{r-1}$?
QUESTION [7 upvotes]: In the formula,
$$\frac{n(n-1)(n-2)\cdots(n-r+2)}{(r-1)!}a^{n-r+1}b^{r-1}$$
what does the "$\cdots$" mean?

REPLY [14 votes]: It means: "There are too many terms to write, but follow the obvious pattern to fill them in". 
In your example, you subtract $1$ from a factor to get the next factor. I might read that aloud as "$n$ times $n-1$ times $n-2$ all the way down to $n-r+2$".
As another example, 
$$
3 + 6 + 9 + \cdots + 3n
$$
would indicate the sum of all positive multiples of $3$ less than or equal to $3n$.

REPLY [2 votes]: Writing it as "$\cdots\;$", would be better than "$\dots\;$" . It indicates a product:
$$
\frac{n(n-1)(n-2) \cdots (n-r+2)}{(r-1)!}a^{n-r+1}b^{r-1}
=\frac{\prod_{k=0}^{r-2} (n-k)}{(r-1)!}a^{n-r+1}b^{r-1}
$$