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Math Help - Series Question

  1. #1
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    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?
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  2. #2
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    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
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  3. #3
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    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.
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  4. #4
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    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.
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