1. ## Series Question

Hey everyone, I have just started learning about sequences and I have found some weird notation. Here is the question (well, a similar one, I'd like to solve the actual one without help).

List the first five terms of the sequence.

$\left\{1 \cdot 2 \cdot 3 \cdot ... \cdot n\right\}$

I'm confused because of the set notation brackets and the fact that it doesn't say $a_n =$ before that.

Am I correct in thinking the answer here is just 1, 2, 6, 24, 120?

2. given $a_n = \{1\times 2 \times \dots \times n \}$

$a_1 = 1$

$a_2 = 1\times 2 = 2$

$a_3 = 1\times 2 \times 3= 6$

then it seems you are correct.

Have you seen factorials?

$n! = n\times (n-1) \times (n-2) \times \dots \times 3\times 2 \times 1$

3. Yes, that's what the notation means. I agree that
$S=\lbrace n! | n \in \mathbb{Z}^+ \rbrace$
would be a lot clearer. That is, S is the set of all factorials of positive integers.

4. Thanks to you both.

Pickslides, I am familiar with factorials, and realize that S_n = n! would have been clearer, I just wanted to give an example using the notation of the problem I must solve.