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Math Help - Sequences & Series

  1. #1
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    Sequences & Series

    I have a simple question about sequence an.

    <br />
an = \frac{(n+2)!}{n!}<br />

    I understand as n goes to infinity the denominator sequence looks like: { 1, 1 * 2, 1 * 2 * 3, ...}

    But what does it do with (n+2)! ?
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  2. #2
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    All I wanna know is what (n + 2)! is when you plug say 1, 2, and 3 in for n.

    If anyone knows, throw me a reply cause I'm lost. (I'm not familiar with the exclamation mark notation.)
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  3. #3
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    ! = Factorial from what I remember it means...

    4! = 1x2x3x4 = 24 etc....

    3! = 1x2x3 = 6 etc...
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  4. #4
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    Quote Originally Posted by justinwager View Post
    ! = Factorial from what I remember it means...

    4! = 1x2x3x4 = 24 etc....

    3! = 1x2x3 = 6 etc...

    Awesome! Thank you. :]
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by freyrkessenin View Post
    I have a simple question about sequence an.

    <br />
an = \frac{(n+2)!}{n!}<br />

    I understand as n goes to infinity the denominator sequence looks like: { 1, 1 * 2, 1 * 2 * 3, ...}

    But what does it do with (n+2)! ?
    Note that (n+2)!=(n+2)(n+1)n!

    So a_n=\frac{(n+2)(n+1){\color{red}n!}}{{\color{red}n  !}}=\dots

    --Chris
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  6. #6
    Grand Panjandrum
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    Quote Originally Posted by freyrkessenin View Post
    I have a simple question about sequence an.

    <br />
an = \frac{(n+2)!}{n!}<br />

    I understand as n goes to infinity the denominator sequence looks like: { 1, 1 * 2, 1 * 2 * 3, ...}

    But what does it do with (n+2)! ?
    So you know that:

    n!=1 \times 2 \times 3 \times ... \times (n-1) \times n

    Then you also know that:

    (n+2)!=1 \times 2 \times 3 \times ... \times (n-1) \times n \times (n+1) \times (n+2)

    and so after cancelling tha common terms:

    <br />
a_n = \frac{(n+2)!}{n!}=(n+1)(n+2)<br />

    n! is the factorial of n and defined as above.

    RonL
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